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Global weak solutions to a phase-field model for motion of grain boundaries

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Applied Mathematics and Mechanics(English Edition) 2022年第11期43卷 1777-1792页

作者： Zixian ZHU Boling GUO Shaomei FANG Department of Mathematics Shanghai UniversityShanghai 200444China Institute of Applied Physics and Computational Mathematics Beijing 100088China College of Mathematics and Information South China Agricultural UniversityGuangzhou 510642China

We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.

关键词： solid-solid phase transition phase-field model Galerkin method weak solutions

L^q Interior Estimates of the Gradient for weak solutions of Quasilinear Elliptic Equations

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Acta Mathematica Sinica,English Series 2007年第12期23卷 2225-2234页

作者： Feng Ping YAO Yong Yong CAI LMAM School of Mathematical Sciences Peking University Bering 100871 P. R. China

The authors present a new proof of L^q interior estimates of the gradient for weak solutions of a quasilinear elliptic equation of p-Laplacian type.

关键词： L^q interior estimates weak solutions quasilinear elliptic maximal function

GLOBAL weak solutions OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

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Acta Mathematica Scientia 2023年第1期43卷 25-42页

作者：酒全森马琳 School of Mathematical Sciences Capital Normal UniversityBeijing100048China

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM)system for quantum fluids with a linear density dependent viscosity in a 3D *** introducing the cold pressure Pc,we prove the global existence of weak solutions with the pressure P+Pc,where P=Aργwithγ≥*** main result extends the one in[13]on the quantum Navier-Stokes equations to the CNSLLM system.

关键词： compressible Navier-Stokes-Landau-Lifshitz-Maxwell equations global existence weak solutions quantum fluid

ON GLOBAL BEHAVIOR OF weak solutions OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS

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Acta Mathematica Scientia 2015年第3期35卷 650-672页

作者：王伟伟 College of Mathematics and Computer Science Fuzhou University

In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.

关键词： Liquid crystals weak solutions bounded absorbing set bounded trajectories attractor

Energy Equality and Uniqueness of weak solutions to MHD Equations in L~∞(O,T;L^n(Ω))

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Acta Mathematica Sinica,English Series 2009年第5期25卷 803-814页

作者： Yan YONG Quan Sen JIU Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P. R. China School of Mathematical Sciences Capital Normal University Beijing 100037 P. R. China

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L∞（0, T; L^n（Ω）. We prove that if the velocity u belongs to the critical space L∞（0, T; L^n（Ω）, the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.

关键词： MHD equations weak solutions energy equality uniqueness

GLOBAL weak solutions TO A THREE-DIMENSIONAL QUANTUM KINETIC-FLUID MODEL

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Acta Mathematica Scientia 2023年第5期43卷 2089-2107页

作者：栗付才李悦孙宝燕 Department of Mathematics Nanjing UniversityNanjing 210093China School of Mathematics and Information Sciences Yantai UniversityYantai 264005China

In this paper,we study a quantum kinetic-fluid model in a three-dimensional *** model is a coupling of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate *** establish a global weak solution to this model for arbitrarily large initial data when the pressure takes the form p(ρ)=ργ+pc(ρ),whereγ>1 is the adiabatic coefficient and pc(ρ)satisfies■for k≥4 and some constant c>0.

关键词： kinetic-fuid model quantum Bohm potential density-dependent viscosity weak solutions

ENERGY CONSERVATION FOR THE weak solutions TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

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Acta Mathematica Scientia 2024年第3期44卷 851-864页

作者：谭忠李心亮杨惠 School of Mathematical Sciences Xiamen UniversityXiamen361005China Shenzhen Research Institute of Xiamen University Shenzhen518057China School of Mathematics and Statistics Shenzhen UniversityShenzhen518060China College of Physics and Optoelectronic Engineering Shenzhen UniversityShenzhen518060China

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in... 详细信息

关键词： compressible nematic liquid crystal flow weak solutions energy conservation

EXISTENCE　OF　weak　solutions　OF　2－D　EULER　EQUATIONS　WITH　INITIAL　VORTICITY　ω_0∈E（log~＋L）~α（α＞0）

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Acta Mathematicae Applicatae Sinica 1996年第2期12卷 121-129页

作者：酒全森 Institute of Applied Mathematics the Chinese Academy of Sciences Beijing China Institute of Mathematics Shantou University Shantou China

It is proved that there exist global weak solutions of 2-D Euler equations in R2 under the assumption that the initial vorticity belongs to a kind of wider spaces, which are Orlicz spaces containing spaces and so on. This result improves on that of [2], [4], [11]. Moreover, these solutions are obtained by vanishing the viscosity term of Navier-Stokes equations.

关键词： Existence Euler equations weak solutions

EXISTENCE OF weak solutions OF 3-D EULER EQUATIONS WITH AXIAL SYMMETRV

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Acta Mathematica Scientia 1999年第1期19卷 107-113页

作者：酒全森

3-D Euler equations is considered in this paper. In cylindrical coordinatesystems, if the components of the velocity fields and scalar function pdo not depend on polar angle θand uθ= 0, author first gives a detailed Proof of someestimates in Section 2 and then obtains the global existence of weak solutions of 3-D Eulerequations in Section 3.

关键词： Existence Euler equations weak solutions