数学物理学报(英文版)

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PREFACE

Zhouping Xin, Tong Yang

数学物理学报(英文版). 2016 (4): 971-972. DOI: 10.1016/S0252-9602(16)30053-4

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GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

李进开, 辛周平

数学物理学报(英文版). 2016 (4): 973-1014. DOI: 10.1016/S0252-9602(16)30054-6

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In this article, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on T², on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.

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TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

金春花, 杨彤

数学物理学报(英文版). 2016 (4): 1015-1029.

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This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

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BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM

丁时进, 黄丙远, 卢友波

数学物理学报(英文版). 2016 (4): 1030-1048. DOI: 10.1016/S0252-9602(16)30056-X

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In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L^∞(0,T;L⁶)-norm of the density of particles and the L¹(0,T;L^∞)-norm of the deformation tensor of velocity gradient.

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THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

王路生, 肖清华, 熊林杰, 赵会江

数学物理学报(英文版). 2016 (4): 1049-1097. DOI: 10.1016/S0252-9602(16)30057-1

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In this article, we are concerned with the construction of global smooth smallamplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in[12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.

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THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM

蒋咪娜, 赖素华, 尹海燕, 朱长江

数学物理学报(英文版). 2016 (4): 1098-1116. DOI: 10.1016/S0252-9602(16)30058-3

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In this article, we are concerned with the stability of stationary solution for outflow problem on the Navier-Stokes-Poisson system. We obtain the unique existence and the asymptotic stability of stationary solution. Moreover, the convergence rate of solution towards stationary solution is obtained. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in space, the solution converges to the corresponding stationary solution as time tends to infinity with the algebraic or the exponential rate in time. The proof is based on the weighted energy method by taking into account the effect of the self-consistent electric field on the viscous compressible fluid.

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GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION

霍朝辉

数学物理学报(英文版). 2016 (4): 1117-1152. DOI: 10.1016/S0252-9602(16)30059-5

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The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space
u_tt-△u+u=-nu, (x,t)∈R³×R₊,
n_tt-△n=△|u|², (x,t)∈R³×R₊,(0.1)
u(x, 0)=u₀(x), ∂_tu(x,0)=u₁(x), n(x,0)=n₀(x), ∂_tn(x,0)=n₁(x),
is considered. It is shown that it is globally well-posed in energy space H ¹×L²×L²×H^-1 if small initial data (u₀(x), u₁(x), n₀(x),n₁(x))∈(H¹×L²×L²×H^-1). It answers an open problem:Is it globally well-posed in energy space H¹×L²×L²×H^-1 for 3D Klein-GordonZakharov equation with small initial data[1, 2]? The method in this article combines the linear property of the equation (dispersive property) with nonlinear property of the equation (energy inequalities). We mainly extend the spaces F^s and N^s in one dimension[3] to higher dimension.

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A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

孔慧慧, 李海梁, 张兴伟

数学物理学报(英文版). 2016 (4): 1153-1166. DOI: 10.1016/S0252-9602(16)30060-1

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In this article, we consider the free boundary value problem of 3D isentropic compressible Navier-Stokes equations. A blow-up criterion in terms of the maximum norm of gradients of velocity is obtained for the spherically symmetric strong solution in terms of the regularity estimates near the symmetric center and the free boundary respectively.

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LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

曹政子, 尹会成, 张麟, 朱露

数学物理学报(英文版). 2016 (4): 1167-1191. DOI: 10.1016/S0252-9602(16)30061-3

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In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable "pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.

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GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY

秦晓红, 王腾, 王益

数学物理学报(英文版). 2016 (4): 1192-1214. DOI: 10.1016/S0252-9602(16)30062-5

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In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ>1 with γ being the adiabatic exponent provided that the wave strength is suitably small.

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GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM

曹文涛, 黄飞敏, 李天虹, 于慧敏

数学物理学报(英文版). 2016 (4): 1215-1224. DOI: 10.1016/S0252-9602(16)30063-7

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In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.

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