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25 August 2016, Volume 36 Issue 4 Previous Issue    Next Issue

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PREFACE Zhouping Xin, Tong Yang Acta mathematica scientia,Series B. 2016, 36 (4):  971-972.  DOI: 10.1016/S0252-9602(16)30053-4 Abstract ( 57 )   RICH HTML PDF   Save Related Articles | Metrics

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GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D Jinkai LI, Zhouping XIN Acta mathematica scientia,Series B. 2016, 36 (4):  973-1014.  DOI: 10.1016/S0252-9602(16)30054-6 Abstract ( 109 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN Chunhua JIN, Tong YANG Acta mathematica scientia,Series B. 2016, 36 (4):  1015-1029.  Abstract ( 67 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM Shijin DING, Bingyuan HUANG, Youbo LU Acta mathematica scientia,Series B. 2016, 36 (4):  1030-1048.  DOI: 10.1016/S0252-9602(16)30056-X Abstract ( 72 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS Lusheng WANG, Qinghua XIAO, Linjie XIONG, Huijiang ZHAO Acta mathematica scientia,Series B. 2016, 36 (4):  1049-1097.  DOI: 10.1016/S0252-9602(16)30057-1 Abstract ( 95 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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THE STABILITY OF STATIONARY SOLUTION FOR OUTFLOW PROBLEM ON THE NAVIER-STOKES-POISSON SYSTEM Mina JIANG, Suhua LAI, Haiyan YIN, Changjiang ZHU Acta mathematica scientia,Series B. 2016, 36 (4):  1098-1116.  DOI: 10.1016/S0252-9602(16)30058-3 Abstract ( 83 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION Zhaohui HUO Acta mathematica scientia,Series B. 2016, 36 (4):  1117-1152.  DOI: 10.1016/S0252-9602(16)30059-5 Abstract ( 61 )   RICH HTML PDF   Save The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space  utt-△u+u=-nu, (x,t)∈R3×R+, ntt-△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 Fs and Ns in one dimension[3] to higher dimension. References | Related Articles | Metrics

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A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY Huihui KONG, Hai-Liang LI, Xingwei ZHANG Acta mathematica scientia,Series B. 2016, 36 (4):  1153-1166.  DOI: 10.1016/S0252-9602(16)30060-1 Abstract ( 75 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS Zhengzi CAO, Huicheng YIN, Lin ZHANG, Lu ZHU Acta mathematica scientia,Series B. 2016, 36 (4):  1167-1191.  DOI: 10.1016/S0252-9602(16)30061-3 Abstract ( 83 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY Xiaohong QIN, Teng WANG, Yi WANG Acta mathematica scientia,Series B. 2016, 36 (4):  1192-1214.  DOI: 10.1016/S0252-9602(16)30062-5 Abstract ( 83 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics

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GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM Wentao CAO, Feimin HUANG, Tianhong LI, Huimin YU Acta mathematica scientia,Series B. 2016, 36 (4):  1215-1224.  DOI: 10.1016/S0252-9602(16)30063-7 Abstract ( 109 )   RICH HTML PDF   Save 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. References | Related Articles | Metrics