Table of Content

25 November 2025, Volume 45 Issue 6 Previous Issue   

For Selected:

View Abstracts

Download Citations EndNote Reference Manager ProCite BibTeX RefWorks

Toggle Thumbnails

Select

PREFACE Zhouqin XIN, Tong YANG Acta mathematica scientia,Series B. 2025, 45 (6):  2301-2304.  DOI: 10.1007/s10473-025-0600-1 Abstract ( 28 )   Save Related Articles | Metrics

Select

GLOBAL STRONG SOLUTIONS TO NAVIER-STOKES/CAHN-HILLIARD EQUATIONS WITH GENERALIZED NAVIER BOUNDARY CONDITION AND DYNAMIC BOUNDARY CONDITION Shijin DING, Yinghua LI, Yuanxiang YAN Acta mathematica scientia,Series B. 2025, 45 (6):  2305-2329.  DOI: 10.1007/s10473-025-0601-0 Abstract ( 35 )   Save In this paper, we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel, which can describe the interaction between a binary material and the walls of the physical domain. We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain. References | Related Articles | Metrics

Select

GLOBAL WEIGHTED SPACE-TIME ESTIMATES OF SMALL DATA WEAK SOLUTIONS TO 1-D SEMILINEAR WAVE EQUATIONS WITH SCALING INVARIANT DAMPINGS Qianqian LI, Huicheng YIN Acta mathematica scientia,Series B. 2025, 45 (6):  2330-2353.  DOI: 10.1007/s10473-025-0602-z Abstract ( 27 )   Save In this paper, for the 1-D semilinear wave equation $\partial_{t}^{2} u-\partial_{x}^{2} u+\frac{\mu}{t} \partial_{t} u=|u|^{p}$ with scaling invariant damping, where $t\ge 1$, $p>1$ and $\mu \in(0,1) \cup\left(1, \frac{4}{3}\right)$, we establish the global weighted space-time estimates as well as the global existence of small data weak solution $u$ when the nonlinearity power $p$ is larger than some critical power $p_{\rm crit}(\mu)$. Our proof is based on a class of new weighted Strichartz estimates with the weight $t^{\theta}\left|(1-\mu)^{2} t^{\frac{2}{|1-\mu|}}-x^{2}\right|^{\gamma}$ ($\theta>0$ and $\gamma>0$ are appropriate constants) for the solution of linear generalized Tricomi equation $\partial_{t}^{2} \phi-t^{m} \partial_{x}^{2} \phi=0$ being any fixed positive number. References | Related Articles | Metrics

Select

ERGODICITY AND WEAK CONVERGENCE OF TRANSITION PROBABILITIES FOR THE 2D PRIMITIVE EQUATIONS WITH MULTIPLICATIVE NOISE Jintao LI, Hongjun GAO Acta mathematica scientia,Series B. 2025, 45 (6):  2354-2390.  DOI: 10.1007/s10473-025-0603-y Abstract ( 25 )   Save This paper investigates the ergodicity and weak convergence of transition proba- bilities for two-dimensional stochastic primitive equations driven by multiplicative noise. The existence of invariant measures is established using the classical Krylov-Bogoliubov theory. The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate. References | Related Articles | Metrics

Select

A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS Qi LI, Wenjun SUN, Song JIANG Acta mathematica scientia,Series B. 2025, 45 (6):  2391-2420.  DOI: 10.1007/s10473-025-0604-x Abstract ( 23 )   Save This paper extends the previous work [1] for the three-temperature gray radiative transfer equations to the frequency-dependent case. Since the additional frequency variable is considered, the equations are more complicated than those in the gray case. Moreover, opacity may be typically a decreasing function of the frequency variable in applications. At the same spatial location, the equations can be in the optically thick case for low frequency photons, while in the optically thin case for high frequency ones. Thus, the resulting discrete equations can significantly increase the computational cost for opacity having the multi-scale property in multiple frequency radiation. Due to the presence of the radiation-electron coupling, electron-ion coupling, and electron-ion diffusion terms, the model under consideration exhibits strong nonlinearity and strong coupling properties. In this paper, the multigroup method is used to discretize the frequency variable and the $H^T_N$ method to discretize the angular variable first. Then, within the framework of a unified gas kinetic scheme (UGKS), a multigroup $H^T_N$-UGKS method is constructed to solve this complex model iteratively. Furthermore, it can be shown that as the Knudsen number tends to zero, with variations in the electron-ion coupling, absorption, and scattering coefficients, the multigroup $H^T_N$-UGKS scheme can converge to numerical schemes for the single-temperature, two-temperature, and the frequency-dependent three-temperature, two-temperature diffusion limit equations, respectively. Finally, several numerical examples are provided to validate the effectiveness and stability of the proposed scheme. References | Related Articles | Metrics

Select

ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL WITH DENSITY-DEPENDENT VISCOSITY AND THERMAL CONDUCTIVITY Huanyuan LI, Junhao ZHANG, Huijiang ZHAO, Jialing ZHU Acta mathematica scientia,Series B. 2025, 45 (6):  2421-2446.  DOI: 10.1007/s10473-025-0605-9 Abstract ( 24 )   Save The radiative Euler equations is a typical model describing the motion of astrophysical flows. For its mathematical studies, it is now well-understood that the radiation effect can indeed induce some dissipative mechanism, which can guarantee the global regularity of smooth solutions to the radiative Euler equations for small initial data. Thus a problem of interest is to see to what extent does the viscosity and/or thermal conductivity influence the global regularity of smooth solutions to the one-dimensional radiative Euler equations for large initial data. For results in this direction, it is shown in [30] that, for a class of state equations, even if a special class of thermal conductivity is further added to the radiative Euler equations, its smooth solutions will still blow up in finite time for large initial data. The main purpose of this paper focuses on the case when both viscosity and thermal conductivity are considered. We first show that, for the state equations and the heat conductivity considered in [30], if the viscosity is further taken into account, the corresponding radiative Navier-Stokes equations does admit a unique global smooth solution for any large initial data provided that the viscosity is a smooth function of the density satisfying certain growth conditions as the density tends to zero and infinity. Moreover, we also show that similar result still holds for the case when the thermodynamics variables satisfy the state equations for ideal polytropic gases, the heat conductivity takes the form studied in [30], and the viscosity is assumed to satisfy the same conditions imposed in the first result. References | Related Articles | Metrics

Select

WELL-POSEDNESS OF THE DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS AND THE KLEIN-GORDON EQUATIONS Yifei WU, Zhibo YANG, Qi ZHOU Acta mathematica scientia,Series B. 2025, 45 (6):  2447-2477.  DOI: 10.1007/s10473-025-0606-8 Abstract ( 19 )   Save The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrödinger and Klein-Gordon equations. These theories encompass both local and global well-posedness, as well as the existence of blowing-up solutions for large and irregular initial data. The main results presented in this paper can be summarized as follows: (1) Discrete Nonlinear Schrödinger Equation: Global well-posedness in $l^p$ spaces for all $1\leq p\leq \infty$, regardless of whether it is in the defocusing or focusing cases. (2) Discrete Klein-Gordon Equation: Local well-posedness in $l^p$ spaces for all $1\leq p\leq \infty$. Furthermore, in the defocusing case, we establish global well-posedness in $l^p$ spaces for any $2\leq p\leq 2\sigma+2$ ($\sigma>0$). In contrast, in the focusing case, we show that solutions with negative energy blow up within a finite time. These conclusions reveal the distinct dynamic behaviors exhibited by the solutions of the equations in discrete settings compared to their continuous setting. Additionally, they illuminate the significant role that discretization plays in preventing ill-posedness, and collapse for the nonlinear Schrödinger equation. References | Related Articles | Metrics

Select

VECTOR ROGUE WAVE PATTERNS OF THE MULTI-COMPONENT NONLINEAR SCHRÖDINGER EQUATION AND GENERALIZED MIXED ADLER-MOSER POLYNOMIALS Huian LIN, Liming LING Acta mathematica scientia,Series B. 2025, 45 (6):  2478-2509.  DOI: 10.1007/s10473-025-0607-7 Abstract ( 19 )   Save This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions for any multi-component nonlinear Schrödinger equation (denoted as $n$-NLSE) with multiple internal large parameters. We report some novel RW patterns, including non-multiple root (NMR)-type patterns with distinct shapes such as semicircular sector, acute sector, pseudo-hexagram, and pseudo-rhombus shapes, as well as multiple root (MR)-type patterns characterized by right double-arrow and right arrow shapes. We demonstrate that these RW patterns are intrinsically related to the root structures of a novel class of polynomials, termed generalized mixed Adler-Moser (GMAM) polynomials, which feature multiple arbitrary free parameters. The RW patterns can be interpreted as straightforward expansions and slight shifts of the root structures for the GMAM polynomials to some extent. In the (x,t)-plane, they asymptotically converge to a first-order RW at the location corresponding to each simple root of the polynomials and to a lower-order RW at the location associated with each multiple root. Notably, the position of the lower-order RW within these patterns can be flexibly adjusted to any desired location in the (x,t)-plane by tuning the free parameters of the corresponding GMAM polynomials. References | Related Articles | Metrics

Select

THE GLOBAL SOLUTION AND BLOWUP OF A EQUATION MODELED FROM THE WATER WAVE PROBLEM WITH CRITICAL GROWTH Zhong TAN, Yiying WANG Acta mathematica scientia,Series B. 2025, 45 (6):  2510-2535.  DOI: 10.1007/s10473-025-0608-6 Abstract ( 16 )   Save In this article, we study the water wave problem with critical growth. We mainly concern with the blowup and asymptotic estimates of the global solution. First, we prove the blow up and decay estimates of the solution with low-energy initial value. Next, we prove the regularity of the global solution with low-energy initial value. In the last part, we study the concentration phenomenon of the global solution no matter with low energy or not by the method of concentration compactness principle. References | Related Articles | Metrics

Select

VANISHING VISCOSITY LIMIT OF A PARABOLIC-ELLIPTIC COUPLED SYSTEM Changjiang ZHU, Qiaolong ZHU Acta mathematica scientia,Series B. 2025, 45 (6):  2536-2548.  DOI: 10.1007/s10473-025-0609-5 Abstract ( 23 )   Save We investigate the vanishing viscosity limit of a parabolic-elliptic coupled system arising in radiation hydrodynamics. The limit is the solution to a hyperbolic-elliptic coupled system. We study the problem on both the whole line $\mathbb{R}$ and the half line $\mathbb{R}_{+}$. Two types of conditions are considered: (1) the initial data are sufficiently close to a given initial state with small wave strength, and (2) the initial data are monotonically increasing. Under these conditions, we establish uniform convergence rates for both Cauchy problems and initial-boundary value problems. Specifically, we demonstrate that the solutions to the parabolic-elliptic system converge to those of the hyperbolic-elliptic system as the viscosity coefficient $\varepsilon$ approaches zero, with convergence rates of $O(\varepsilon^\frac{3}{4})$ for $u$ and $O(\varepsilon)$ for $q$ in $L^\infty$-norm. Additionally, we prove the global well-posedness of the parabolic-elliptic coupled system by the maximum principle and energy method. Our results extend previous work by providing explicit convergence rates and addressing both Cauchy problems and initial-boundary value problems under various conditions. References | Related Articles | Metrics

Select

MARTINGALE SOLUTIONS OF FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS DRIVEN BY SUPERLINEAR NOISE Bixiang WANG Acta mathematica scientia,Series B. 2025, 45 (6):  2549-2578.  DOI: 10.1007/s10473-025-0610-z Abstract ( 20 )   Save In this paper, we prove the existence of martingale solutions of a class of stochas-tic equations with a monotone drift of polynomial growth of arbitrary order and a continuous di_usion term with superlinear growth. Both the nonlinear drift and di_usion terms are not required to be locally Lipschitz continuous. We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-di_usion equation with polynomial drift driven by a superlinear noise. The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions de_ned by the Galerkin method. References | Related Articles | Metrics

Select

ON STATIC LIQUID LANE-EMDEN STARS Shuang MIAO, Yangyang WANG Acta mathematica scientia,Series B. 2025, 45 (6):  2579-2590.  DOI: 10.1007/s10473-025-0611-y Abstract ( 20 )   Save The liquid Lane-Emden star is a free boundary problem of compressible Euler-Poisson equation which describes motion of celestial bodies. This model admits a class of static solutions parametrized by its central density. According to Lam [9], when the central density is sufficiently small or the adiabatic constant $\gamma\in [\frac43,2]$, the static solutions are linearly stable. In this article, by constructing periodic solutions to the linearized equation, we prove that even though these solutions are linearly stable, they may not decay in time. Moreover we prove that if the sum of the internal energy and potential energy of this model has an minimizer, then it must be the spherically symmetric solution to the static equation, therefore demonstrating their stability from a variational point of view. References | Related Articles | Metrics

Select

EXISTENCE OF LARGE BOUNDARY LAYER SOLUTIONS TO INFLOW PROBLEM OF 1D FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS Yi WANG, Yongfu YANG, Qiuyang YU Acta mathematica scientia,Series B. 2025, 45 (6):  2591-2606.  DOI: 10.1007/s10473-025-0612-x Abstract ( 16 )   Save We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional (1D) full compressible Navier-Stokes equations on a half line $\mathbb{R}_+$. Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results, the delicate global phase plane analysis, based on the qualitative theory of ODEs, is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic, transonic, and subsonic regions, respectively, which completely answers the existence/non-existence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations. References | Related Articles | Metrics

Select

REGULARIZATION EFFECT OF THE BOLTZMANN EQUATION UNDER NAVIER-STOKES TYPE SCALING Qi AN, Xin HU, Weixi LI Acta mathematica scientia,Series B. 2025, 45 (6):  2607-2628.  DOI: 10.1007/s10473-025-0613-9 Abstract ( 16 )   Save We investigate the smoothing effect of the spatially inhomogeneous Boltzmann equation without an angular cut-off, under the Navier-Stokes scaling. For Maxwellian molecules or hard potentials with singular angular kernels, we demonstrate that the solutions become analytic at positive times when the angular singularities are sufficiently strong and lie within the optimal Gevrey class when the singularities are mild. The analysis is based on carefully selected vector fields with time-dependent coefficients and quantitative estimates of directional derivatives, which reveal the behavior of the kinetic-fluid transition. References | Related Articles | Metrics

Select

GLOBAL CLASSICAL SOLUTION FOR THE VLASOV-EULER-MAXWELL-FOKKER-PLANCK SYSTEM Jiamu DUAN, Shuangqian LIU, Yating WANG, Xueying ZHANG Acta mathematica scientia,Series B. 2025, 45 (6):  2629-2649.  DOI: 10.1007/s10473-025-0614-8 Abstract ( 18 )   Save This paper investigates a coupled system consisting of the Vlasov-Fokker-Planck equation, the compressible Euler equations for uid dynamics, and the Maxwell equations for plasma dynamics. We establish the global well-posedness of the Cauchy problem within a perturbative framework. The proof relies on a re_ned energy method, which provides uniform control over the solution and ensures the global existence. References | Related Articles | Metrics

Select

STABILITY ANALYSIS OF THE COMPRESSIBLE EULER-EULER SYSTEM AROUND PLANAR COUETTE FLOW Hailiang LI, Jingyang SUN, Deyang ZHANG, Shuang ZHAO Acta mathematica scientia,Series B. 2025, 45 (6):  2650-2668.  DOI: 10.1007/s10473-025-0615-7 Abstract ( 23 )   Save In this paper, we investigate the linear stability/instability of the planar Couette flow to the two-dimensional compressible Euler-Euler system for $(\rho,{u})$ and $(n,{v})$ with the sound speeds $c_1$ and $c_2$ respectively, coupled each other through the drag force on $\mathbb{T} \times \mathbb{R}$. It is shown in general for the different sound speeds $c_1 \neq c_2$ that the perturbations of the densities $(\rho,n)$ and the velocities $({u},{v})$ demonstrate the stability in any fixed finite time interval $(0,T]$, besides, excluding the zero mode, the densities $(\rho, n)$ and the irrotational components of the velocities $({u},{v})$ obey the algebraic time-growth rates, while the rotational components of the velocities $({u},{v})$ exhibit the algebraic time-decay rates due to the inviscid damping. For the case $c_1=c_2$ (same sound speeds), it is proved that the relative velocity ${u}-{v}$ decays faster than those of the velocities ${u},{v}$ caused by the inviscid damping, but the linear instability of the densities $(\rho, n)$ and the irrotational components of the velocities $({u},{v})$ is also shown for some large time in spite of the inviscid damping. References | Related Articles | Metrics

Select

A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM Quoc-Hung NGUYEN, Dongyi WEI, Zhifei ZHANG Acta mathematica scientia,Series B. 2025, 45 (6):  2669-2684.  DOI: 10.1007/s10473-025-0616-6 Abstract ( 18 )   Save This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational work of Ionescu, Pausader, Wang and Widmayer [28], we provide a streamlined proof of nonlinear Landau damping for the 3D unscreened VP system. Our analysis leverages sharp decay estimates, novel decomposition techniques to demonstrate the stabilization of the particle distribution and the decay of electric field. These results reveal the free transport-like behavior for the perturbed density $\rho(t,x)$, and enhance the understanding of Landau damping in an unconfined setting near stable equilibria. References | Related Articles | Metrics

Select

ASYMPTOTIC STABILITY OF GLOBAL SOLUTIONS FOR A CLASS OF SEMILINEAR WAVE EQUATION Mutong HE, Feimin HUANG, Tianyi WANG Acta mathematica scientia,Series B. 2025, 45 (6):  2685-2714.  DOI: 10.1007/s10473-025-0617-5 Abstract ( 22 )   Save This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux. The global solution is shown to converge to a combination of a rarefaction wave and a viscous contact wave as time tends to infinity by employing the $L^2$ energy method and a refined wave interaction analysis. This is the first result on the asymptotics toward multiwave for the damped wave equation, and this asymptotic stability result does not rely on the small assumption of neither the initial perturbations nor the wave strength. References | Related Articles | Metrics