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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 （341） 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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GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES Min HE, Maofa WANG, Jiale CHEN Acta mathematica scientia,Series B 2025, 45 (2): 291-309.   DOI: 10.1007/s10473-025-0201-z Abstract （273） In this paper, we study composition operators on weighted Bergman spaces of Dirichlet series. We first establish some Littlewood-type inequalities for generalized mean counting functions. Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series. The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained. 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 （179） 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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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 （161） 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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CERTAIN OSCILLATING OPERATORS ON HERZ-TYPE HARDY SPACES Ziyao LIU, Dashan FAN Acta mathematica scientia,Series B 2025, 45 (2): 310-326.   DOI: 10.1007/s10473-025-0202-y Abstract （137） Let $0 ＜p\leq1＜q＜\infty$, and $\omega_{1},\omega_{2}\in A_{1}$ (Muckenhoupt-class). We study an oscillating multiplier operator $T_{\gamma ,\beta }$ and obtain that it is bounded on the homogeneous weighted Herz-type Hardy spaces $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n};\omega _{1},\omega _{2})$ when $\gamma=\frac{n\beta }{2}, \alpha =n(1-1/q)$. Also, for the unweighted case, we obtain the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of $T_{\gamma ,\beta }$ under certain conditions on $\gamma$. These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun. As an application, we prove the $H\dot{K}_{q}^{\alpha ,p}(\mathbb{R}^{n})$ boundedness of the spherical average $S_{t}^{\delta}$ uniformly on $t>0$. 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 （112） 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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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 （108） 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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${C^{1, 1}}$ REGULARITY FOR SOLUTIONS TO THE DEGENERATE DUAL ORLICZ-MINKOWSKI PROBLEM Di WU Acta mathematica scientia,Series B 2025, 45 (2): 327-337.   DOI: 10.1007/s10473-025-0203-x Abstract （107） In this paper, $C^{1, 1}$ regularity for solutions to the degenerate dual Orlicz-Minkowski problem is considered. The dual Orlicz-Minkowski problem is a generalization of the $L_p$ dual Minkowski problem in convex geometry. The proof is adapted from Guan-Li [17] and Chen-Tu-Wu-Xiang [11]. 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 （106） 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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THE GLOBAL DYNAMICS OF A 3-DIMENSIONAL DIFFERENTIAL SYSTEM IN $\mathbb{R}^3$ VIA A DARBOUX INVARIANT Jaume LIBRE, Claudia VALLS Acta mathematica scientia,Series B 2025, 45 (2): 338-346.   DOI: 10.1007/s10473-025-0204-9 Abstract （105） The differential system $\dot x= ax -y z, \ \dot y = -b y + x z, \ \dot z= -c z + x^2,$ where $a$, $b$ and $c$ are positive real parameters, has been studied numerically due to the big variety of strange attractors that it can exhibit. This system has a Darboux invariant when $c=2b$. Using this invariant and the Poincaré compactification technique we describe analytically its global dynamics. 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 （101） 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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BRAKE ORBITS WITH MINIMAL PERIOD ESTIMATES OF FIRST-ORDER ANISOTROPIC HAMILTONIAN SYSTEMS Xiaofei ZHANG, Chungen LIU Acta mathematica scientia,Series B 2025, 45 (2): 347-362.   DOI: 10.1007/s10473-025-0205-8 Abstract （100） In this paper, the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth, i.e., the Hamiltonian functions may have super-quadratic, sub-quadratic and quadratic behaviors simultaneously in different variable components. Reference | Related Articles | Metrics | Comments（0）

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MOUNTAIN-PASS SOLUTION FOR A KIRCHHOFF TYPE ELLIPTIC EQUATION Lifu WENG, Xu ZHANG, Huansong ZHOU Acta mathematica scientia,Series B 2025, 45 (2): 385-400.   DOI: 10.1007/s10473-025-0207-6 Abstract （96） We are concerned with a nonlinear elliptic equation, involving a Kirchhoff type nonlocal term and a potential $V(x)$, on $\mathbb{R}^3$. As is well known that, even in $H^1_r(\mathbb{R}^3)$, the nonlinear term is a pure power form of $|u|^{p-1}u$ and $V(x)\equiv 1$, it seems very difficult to apply the mountain-pass theorem to get a solution (i.e., mountain-pass solution) to this kind of equation for all $p\in(1,5)$, due to the difficulty of verifying the boundedness of the Palais-Smale sequence obtained by the mountain-pass theorem when $p\in(1,3)$. In this paper, we find a new strategy to overcome this difficulty, and then get a mountain-pass solution to the equation for all $p\in(1,5)$ and for both $V(x)$ being constant and nonconstant. Also, we find a possibly optimal condition on $V(x)$. Reference | Related Articles | Metrics | Comments（0）

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INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS Chong LI, Yi PENG, Helen W.J. ZHANG Acta mathematica scientia,Series B 2025, 45 (2): 737-754.   DOI: 10.1007/s10473-025-0225-4 Abstract （95） In this paper, we examine the functions $a(n)$ and $b(n)$, which respectively represent the number of cubic partitions and cubic partition pairs. Our work leads to the derivation of asymptotic formulas for both $a(n)$ and $b(n)$. Additionally, we establish the upper and lower bounds of these functions, factoring in the explicit error terms involved. Crucially, our findings reveal that $a(n)$ and $b(n)$ both satisfy several inequalities such as log-concavity, third-order Turán inequalities, and strict log-subadditivity. Reference | Related Articles | Metrics | Comments（0）

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A SINGULAR ENERGY LINE OF POTENTIAL WELL ON EVOLUTIONARY $ p$-LAPLACIAN WITH LOGARITHMIC SOURCE Gege LIU, Jingxue YIN, Yong LUO Acta mathematica scientia,Series B 2025, 45 (2): 363-384.   DOI: 10.1007/s10473-025-0206-7 Abstract （90） We consider large-time behaviors of weak solutions to the evolutionary $p$-Laplacian with logarithmic source of time-dependent coefficient. We find that the weak solutions may neither decay nor blow up, provided that the initial data $u(\cdot,t_0)$ is on the Nehari manifold $\mathscr{N}:=\big\{v\in W_0^{1,p}(\Omega): I(v,t_0)=0, \|\nabla v\|_p^p\neq0 \big\}$. This is quite different from the known results that the weak solutions may blow up as $u(\cdot, t_0)\in \mathscr{N}^{-}:=\big\{v\in W_0^{1,p}(\Omega): I(v,t_0)<0\big\}$ and weak solutions may decay as $u(\cdot, t_0)\in\mathscr{N}^{+}:=\big\{v\in W_0^{1,p}(\Omega): I(v,t_0)>0\big\}$. Reference | Related Articles | Metrics | Comments（0）

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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 （86） 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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OPTIMAL DECAY RATES FOR THE WEAK SOLUTIONS OF THE FLOCKING PARTICLES COUPLED WITH INCOMPRESSIBLE VISCOUS FLUID MODELS Houzhi TANG, Shuxing ZHANG, Weiyuan ZOU Acta mathematica scientia,Series B 2025, 45 (2): 659-683.   DOI: 10.1007/s10473-025-0221-8 Abstract （79） This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in $\mathbb{R}^3$. First, we obtain the global weak solution using the characteristic and energy methods. Then, under the small assumption of the mass of the particle, we show that the solutions decay at the algebraic time-decay rate. Finally, it is also proved that the above rate is optimal. It should be remarked that if the particle in the coupled system vanishes (i.e. $f=0$), our works coincide with the classical results by Schonbek [32] (J Amer Math Soc, 1991, 4: 423-449), which can be regarded as a generalization from a single fluid model to the two-phase fluid one. 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 （79） 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 （78） 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）