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ON BLOW-UP TO THE ONE-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH DEGENERATE VISCOSITY AND VACUUM Yue CAO, Yachun LI, Shaojun YU Acta mathematica scientia,Series B 2025, 45 (4): 1343-1354.   DOI: 10.1007/s10473-025-0406-1 Abstract （406） In this paper, we consider the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum in $\mathbb{R}$, where the viscosity depends on the density in a super-linear power law (i.e., $\mu(\rho)=\rho^\delta, \delta>1$). We first obtain the local existence of the regular solution, then show that the regular solution will blow up in finite time if initial data have an isolated mass group, no matter how small and smooth the initial data are. It is worth mentioning that based on the transport structure of some intrinsic variables, we obtain the $L^\infty$ bound of the density, which helps to remove the restriction $\delta\leq \gamma$ in Li-Pan-Zhu [21] and Huang-Wang-Zhu [13]. Reference | Related Articles | Metrics | Comments（0）

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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 （313） 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. Reference | Related Articles | Metrics | Comments（0）

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GLOBAL WELL-POSEDNESS OF 3D INCOMPRESSIBLE HYPER-DISSIPATIVE HALL-MHD EQUATIONS IN ANISOTROPIC BESOV SPACES Dezai MIN, Qingkai WANG, Gang WU, Zhuoya YAO Acta mathematica scientia,Series B 2025, 45 (5): 1723-1751.   DOI: 10.1007/s10473-025-0501-3 Abstract （221） In this paper, we investigate the well-posedness result of the three-dimensional incompressible hyper-dissipative Hall-Magnetohydrodynamic equations with small anisotropic derivative. Making using of anisotropic Littlewood-Paley theory, we conclude that the hyper-dissipative Hall-MHD system has a unique global solution provided that $$\begin{align*} \left(\|J_{0}\|_{\mathcal{B}^{1-2\alpha}_{2}}+\|(\Lambda_{h}^{-1}\partial_{3}u_{0}, B_{0}^{h})\|_{\mathcal{B}^{1-2\alpha}_{2}}\right) \cdot F(u_{0}, B_{0}) \end{align*}$$ is sufficiently small. Here, $F(u_{0}, B_{0})$ is a bounded function, which depends on $\|(u_{0}, B_{0})\|_{\mathcal{B}^{1-2\alpha}_{2}}$ and $\|u_{0}^{h}\|_{H^{1}}$. Reference | Related Articles | Metrics | Comments（0）

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ASYMPTOTIC STABILITY OF COUETTE FLOW WITH NAVIER-SLIP BOUNDARY CONDITIONS FOR 2-D BOUSSINESQ SYSTEM VIA RESOLVENT ESTIMATE Gaofeng WANG Acta mathematica scientia,Series B 2025, 45 (5): 1752-1773.   DOI: 10.1007/s10473-025-0502-2 Abstract （135） In this paper, we study the nonlinear stability problem for the two-dimensional Boussinesq system around the Couette flow in a finite channel with Navier-slip boundary condition for the velocity and Dirichlet boundary condition for the temperature with small viscosity $\nu$ and small thermal diffusion $\mu$. We establish that if the initial perturbation velocity and initial perturbation temperature satisfy $$\|u_{0}\|_{H^2}\leq \epsilon_0\min\left\lbrace \mu,\nu\right\rbrace ^{\frac{1}{2}},$$ and $$\quad \|\theta_{0}\|_{H^1}+\| |D_x|^{\frac{1}{3}}\theta_{0}\|_{H^1}\leq \epsilon_1\min\left\lbrace \mu,\nu\right\rbrace ^{\frac{5}{6}},$$ for some small $\epsilon_0$ and $\epsilon_1$ independent of $\mu,\nu$, then the solution of the two-dimensional Navier-Stokes Boussinesq system does not transition away from the Couette flow for any time. Reference | Related Articles | Metrics | Comments（0）

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MULTIPLE NORMALIZED SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH COMPETING POWER NONLINEARITY Huifang JIA, Chunjiang ZHENG Acta mathematica scientia,Series B 2025, 45 (5): 1961-1980.   DOI: 10.1007/s10473-025-0510-2 Abstract （135） In this paper, we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations $$\begin{equation*} \begin{cases} (-\Delta)^{s} u+\lambda u=|u|^{p-2}u-|u|^{q-2}u,\ \ x\in \mathbb{R}^{N},\\ \displaystyle \int_{\mathbb{R}^{N}}|u|^{2}{\rm d}x=c>0,\\ \end{cases}\tag{$P$} \end{equation*}$$ where $N\geq 2$, $s\in (0,1)$, $2+\frac{4s}{N}<p<q\leq 2_{s}^{*}=\frac{2N}{N-2s}$, $(-\Delta)^{s}$ represents the fractional Laplacian operator of order $s$, and the frequency $\lambda\in \mathbb{R}$ is unknown and appears as a Lagrange multiplier. Specifically, we show that there exists a $\hat{c}>0$ such that if $c>\hat{c}$, then the problem ($P$) has at least two normalized solutions, including a normalized ground state solution and a mountain pass type solution. We mainly extend the results in [Commun Pure Appl Anal, 2022, 21: 4113-4145], which dealt with the problem ($P$) for the case $2<p<q<2+\frac{4s}{N}$. Reference | Related Articles | Metrics | Comments（0）

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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 （133） 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. Reference | Related Articles | Metrics | Comments（0）

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AN INEXACT SYMMETRIC PROXIMAL ADMM WITH CONVEX COMBINATION PROXIMAL CENTERS FOR SEPARABLE CONVEX PROGRAMMING Jinbao JIAN, Xianke TANG, Jianghua YIN, Xianzhen JIANG Acta mathematica scientia,Series B 2025, 45 (4): 1701-1722.   DOI: 10.1007/s10473-025-0424-z Abstract （132） In this paper, we develop an inexact symmetric proximal alternating direction method of multipliers (ISPADMM) with two convex combinations (ISPADMM-tcc) for solving two-block separable convex optimization problems with linear equality constraints. Specifically, the convex combination technique is incorporated into the proximal centers of both subproblems. We then approximately solve these two subproblems based on relative error criteria. The global convergence, and $O(\frac{1}{N})$ ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions, where $N$ denotes the number of iterations. Finally, numerical experiments on solving the $l_1$-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method. Reference | Related Articles | Metrics | Comments（0）

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DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL Lei LI, Zhengce ZHANG Acta mathematica scientia,Series B 2025, 45 (4): 1284-1306.   DOI: 10.1007/s10473-025-0404-3 Abstract （127） We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball in $\mathbb{R}^{3}$ with one-speed velocity. The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature. For the $O(\epsilon)$ boundary data of the intensity of the radiation and the suitable small boundary data of the temperature, we prove the existence, uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model. Reference | Related Articles | Metrics | Comments（0）

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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 （124） 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. Reference | Related Articles | Metrics | Comments（0）

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EXISTENCE AND STABILITY ANALYSIS OF  EVOLUTIONARY DIFFERENTIAL HEMIVARIATIONAL INEQUALITIES IN BANACH SPACES Wei LI, Ke XU, Rong HU, Zhiyang MA Acta mathematica scientia,Series B DOI: 10.1007/s10473-026-0203-5 Accepted: 19 October 2025

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PREFACE Zhouqin XIN, Tong YANG Acta mathematica scientia,Series B 2025, 45 (6): 2301-2304.   DOI: 10.1007/s10473-025-0600-1 Abstract （118） Related Articles | Metrics | Comments（0）

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GLOBAL SOLUTION TO THE 3D ANISOTROPIC INCOMPRESSIBLE MHD SYSTEM WITH PARTIAL AND FRACTIONAL DISSIPATION Yanping ZHOU, Pingping GUI, Huiyang SONG Acta mathematica scientia,Series B Accepted: 21 October 2025

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A POSITIVE SOLUTION FOR QUASILINEAR SCHRÖODINGER-POISSON SYSTEM WITH CRITICAL EXPONENT Lanxin HUANG, Jiabao SU Acta mathematica scientia,Series B 2025, 45 (4): 1247-1264.   DOI: 10.1007/s10473-025-0402-5 Abstract （112） In this paper, we study the quasilinear Schrödinger-Poisson system with critical Sobolev exponent $$\begin{aligned} \begin{cases} -\Delta_{p} u+|u|^{p-2}u+l(x)\phi |u|^{p-2}u=|u|^{p^{*}-2}u+\mu h(x)|u|^{q-2}u & \ \ \ \mathrm{in}\ \mathbb{R}^{3},\\ -\Delta \phi=l(x)|u|^{p} &\ \ \ \mathrm{in}\ \mathbb{R}^{3}, \end{cases} \end{aligned}$$ where $\mu >0$, $\frac{3}{2}<p<3$, $p\leqslant q<p^{*}=\frac{3p}{3-p}$ and $\Delta_{p} u= \hbox{div}(|\nabla u|^{p-2}\nabla u)$. Under certain assumptions on the functions $l$ and $h$, we employ the mountain pass theorem to establish the existence of positive solutions for this system. Reference | Related Articles | Metrics | Comments（0）

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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 （104） 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. Reference | Related Articles | Metrics | Comments（0）

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PROOFS OF CONJECTURES ON RAMANUJAN-TYPE SERIES OF LEVEL 3 John M. CAMPBELL Acta mathematica scientia,Series B 2025, 45 (4): 1482-1496.   DOI: 10.1007/s10473-025-0413-2 Abstract （103） The level 3 case for Ramanujan-type series has been considered as the most mysterious and the most challenging, out of all possible levels for Ramanujan-type series. This motivates the development of new techniques for constructing Ramanujan-type series of level 3. Chan and Liaw introduced an alternating analogue of the Borwein brothers' identity for Ramanujan-type series of level 3; subsequently, Chan, Liaw, and Tian formulated another proof of the Chan--Liaw identity, via the use of Ramanujan's class invariant. Using the elliptic lambda function and the elliptic alpha function, we prove, via a limiting case of the Kummer--Goursat transformation, a new identity for evaluating the summands for alternating Ramanujan-type series of level 3, and we apply this new identity to prove three conjectured formulas for quadratic-irrational, Ramanujan-type series that had been discovered via numerical experiments with Maple in 2012 by Aldawoud. We also apply our identity to prove a new Ramanujan-type series of level 3 with a quartic convergence rate and quartic coefficients. Reference | Related Articles | Metrics | Comments（0）

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INTERFACE DYNAMICS IN NONLOCAL DISPERSAL FISHER-KPP EQUATIONS Wen TAO, Wantong LI, Jianwen SUN, Wenbing XU Acta mathematica scientia,Series B 2025, 45 (5): 1774-1813.   DOI: 10.1007/s10473-025-0503-1 Abstract （99） It is well-known that the propagation phenomena of nonlocal dispersal equations have been extensively studied, and the known results on the interface dynamics of this equation are under the compactly supported initial value. Moreover, there was no explicit formula regarding the interface due to the peculiarity of nonlocal dispersal operators. A natural question is whether it is possible to provide a precise characterization of the interface with respect to small parameter for the general initial values (including exponentially bounded and unbounded). This paper is concerned with the interface dynamics of the nonlocal dispersal equation with scaling parameter. For the exponentially bounded initial value, by choosing the hyperbolic scaling, we show that at a very small time, the interface is confined within a generated layer whose thickness is at most ${O}(\sqrt{\varepsilon}\vert\ln \varepsilon\vert)$, and subsequently, the interface propagates at a linear speed determined by the decay rate of initial value. For a class of exponentially unbounded initial value, Reference | Related Articles | Metrics | Comments（0）

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BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES Jiaxin LIU, Guantie DENG, Zhiqiang GAO Acta mathematica scientia,Series B 2025, 45 (4): 1235-1246.   DOI: 10.1007/s10473-025-0401-6 Abstract （93） We explore some necessary and sufficient conditions for the boundedness of the Forelli-Rudin type operator $T$ on the weighted Lebesgue space associated with tubular domains over the forward light cone. Our approach involves conducting precise computations for a series of complex integrals to identify appropriate test functions, and through a detailed analysis of these test functions, we derive the boundedness properties of the operator $T$. This work is significant in the study of the Bergman projection operators. Reference | Related Articles | Metrics | Comments（0）

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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 （90） 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. Reference | Related Articles | Metrics | Comments（0）

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NONEXISTENCE AND EXISTENCE OF SUPERSOLUTIONS FOR HIGHER ORDER SEMILINEAR EQUATIONS IN EXTERIOR DOMAINS Xianmei ZHOU Acta mathematica scientia,Series B 2025, 45 (5): 1920-1941.   DOI: 10.1007/s10473-025-0508-9 Abstract （88） In this paper, we study the weighted higher order semilinear equation in an exterior domain $$\begin{equation*} (-\Delta)^{m} u=|x|^{\alpha}g(u) \quad \quad \text{in} \ \mathbb{R}^{N}\setminus B_{R_{0}}, \end{equation*}$$ where $N\geq1$, $m\geq2$ are integers, $\alpha>-2m$, $g$ is a continuous and nondecreasing function in $\left[ 0,+\infty\right) $ and positive in $\left( 0,+\infty\right) $, $ B_{R_{0}}$ is the ball of the radius $R_{0}$ centered at the origin. We prove that a positive supersolution of the problem which verifies $ (-\Delta )^{i}u > 0 $ in $\ \mathbb{R}^{N}\setminus B_{R_{0}}$ $(i=0,\cdots, m-1)$ exists if and only if $N>2m$ and $$\begin{equation*} \int_{0}^{\delta}\frac{g(t)}{t^{\frac{2(N-m)+\alpha}{N-2m}}}{\rm d}t<\infty, \end{equation*}$$ for some $\delta>0$. We further obtain some existence and nonexistence results for the positive solution to the Dirichlet problem when $g(u)=u^p$ with $p>1 $, by using the Pohozaev identity and an embedding lemma of radial Sobolev spaces. Reference | Related Articles | Metrics | Comments（0）

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ON THE CONCENTRATION OF STANDING WAVES FOR NLS EQUATION WITH POINT-DIPOLE POTENTIAL Jun WANG, Xiaoguang LI Acta mathematica scientia,Series B 2025, 45 (4): 1265-1283.   DOI: 10.1007/s10473-025-0403-4 Abstract （88） We study the following minimization problem: $$d_{p}(M_{p}):=\inf\{E_{p}(u): \|u\|_{L^{2}}=M_{p}\},$$ where the Gross-Pitaevskii energy functional $$E_{p}(u)=\int_{\mathbb{R}^{N}}|\nabla u|^{2}-c\frac{|u|^{2}}{|x|^{2}}+V(x)|u|^{2}{\rm d}x-\frac{2}{p+2}\int_{\mathbb{R}^{N}}|u|^{p+2}{\rm d}x.$$ When $p=p^{*}:=\frac{4}{N}$, the precise concentration behavior of minimizers is analyzed as $M_{p^{*}}\nearrow \|Q_{p^{*}}\|_{L^{2}}$, where $Q_{p^{*}}$ is the unique radially positive solution of $-\Delta \varphi-c\frac{\varphi}{|x|^{2}}-|\varphi|^{p^{*}+1}\varphi=0$. When $0<p<p^{*}$, we prove that all minimizers must blow up if $\lim\limits_{p\to p^{*}}M_{p}\geq \|Q_{p^{*}}\|_{L^{2}}$. On this argument, the detailed concentration behavior of minimizers is established as $p\nearrow p^{*}$. Reference | Related Articles | Metrics | Comments（0）