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A global weak solution to the Lorentzian harmonic map flow

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Science China Mathematics 2020年第1期63卷 155-166页

作者： Xiaoli Han Lei Liu Liang Zhao Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Max Planck Institute for Mathematics in the Sciences Leipzig 04103Germany School of Mathematical Sciences Laboratory of Mathematics and Complex Systems of MOEBeijing Normal UniversityBeijing 100875China

We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product *** prove that there exists a unique... 详细信息

关键词： harmonic map heat flow Lorentzian manifold warped product blow up weak solution

The Existence and Long-Time Behavior of weak solution to Bipolar Quantum Drift-Diffusion Model

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Chinese Annals of Mathematics,Series B 2007年第6期28卷 651-664页

作者： Xiuqing CHEN Li CHEN Huaiyu JIAN School of Sciences Beijing University of Posts and Telecommunications Beijing 100876 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic *** semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary ***,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.

关键词： Quantum drift-diffusion weak solution Long-time behavior

weak solution of Generalized KdV Equation with High Order Perturbation Terms

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Chinese Quarterly Journal of Mathematics 2011年第1期26卷 39-45页

作者： CHENG Jun-xiang WANG Yan-hong School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454000China

By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturb... 详细信息

关键词： generalized KdV equation with high order perturbation terms weak solution compensated compactness

Existence of weak solution for p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-like Operator by Topological Degree

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Journal of Partial Differential Equations 2023年第2期36卷 203-219页

作者： EL OUAARABI Mohamed ALLALOU Chakir MELLIANI Said Applied Mathematics and Scientific Computing Laboratory Faculty of Sciences and TechniquesSultan Moulay Slimane UniversityBeni MellalMorocco

In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary *** a topological degree for a class of demicontinuous operator of generalized(S_(+))type and the theory of the variable exponent Sobolev space,we establish the existence of"weak solution"of this problem.

关键词： p(x)-Kirchhoff type problem p(x)-Laplacian-like operator weak solution topological degree methods variable exponent Sobolev space

Large Time Behavior of a weak solution for Non-Newtonian Flow

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Northeastern Mathematical Journal 2006年第3期22卷 306-322页

作者：吴珞刘辉昭王宗尧 Department of Mathematics East China University of Science and Technology Department of Mathematics Hebei University of Technology

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvaiue of the Stokes operator.

关键词： large time behavior non-Newtonian flow weak solution

Well-Posedness of Stochastic Continuity Equations on Riemannian Manifolds

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Chinese Annals of Mathematics,Series B 2024年第1期45卷 81-122页

作者： Luca GALIMBERTI Kenneth H.KARLSEN Department of Mathematical Sciences NTNU Norwegian University of Science and TechnologyN-7491 TrondheimNorway Department of mathematics University of OsloP.O.Box 1053BlindernN-0316 OsloNorway

The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed Riemannian manifold M with metric *** velocity field u is perturbed by Gaussian noise terms Wi(t),:WN(t)driven by smooth spatially dependent vector fields a1(x),...,aN(x)on *** velocity u belongs to L_(t)^(1)W_(x)^(1,2)with divh u bounded in Lf,for p>d+2,where d is the dimension of M(they do not assume div_(h) u∈L_(t,x)^(∞)).For carefully chosen noise vector fields ai(and the number N of them),they show that the initial-value problem is well-posed in the class of weak L^(2) solutions,although the problem can be ill-posed in the deterministic case because of concentration *** proof of this“regularization by noise”result is based on a L^(2) estimate,which is obtained by a duality method,and a weak compactness argument.

关键词： Stochastic continuity equation Riemannian manifold Hyperbolic equa-tion Non-smooth velocity field weak solution Existence Uniqueness

weak-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

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Acta Mathematica Scientia 2024年第4期44卷 1415-1440页

作者： Fan YANG Congming LI School of Mathematical Sciences CMA-ShanghaiShanghai Jiao Tong UniversityShanghai 200240China

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these *** this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

关键词： analysis of parabolic and elliptic types weak-strong uniqueness active liquid crystals weak solution energy equality

THE solution OF weak FORMULATION FOR AXISYMMETRIC PROBLEM OF ORTHOTROPIC CANTILEVER CYLINDRICAL SHELL

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Applied Mathematics and Mechanics(English Edition) 1999年第6期20卷 34-40页

作者：丁克伟唐立民 Research Institute of Engineering Mechanics Dalian University of Technology 116023 Dalian P R China

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ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｍａｌｓｔｒｅｓｅｓｏｆｉｓｏｔｒｏｐｉｃａｎｄｏｒｔｈｏｔｒｏｐｉｃｃｙｌｉｎｄｒｉｃａｌｓｈｅｌｈａｖｅｂｅｎｓｔｕｄｉｅｄｉｎｒｅｆｅｒｅｎｃｅｓ［１～３］ｂｙｕｓｉｎｇｔｈｒｅ＿ｄｉｍｅｎｓｉｏｎａｌｅｌａｓｔ...

关键词： axisymmetric problem closed cantilever cylindrical shell mixed equation O343.1 thermal stresses weak solution

weak solutions on Lorentzian 2-tori

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Acta Mathematica Sinica,English Series 2017年第10期33卷 1352-1360页

作者： Liang JIN Xiaojun CUI Department of Mathematics Nanjing University Nanjing 210093 P. R. China

In this paper, we classify the set of Lorentzian metrics on T2, analyse the topological structure of some subclasses and study whether a subclass could admit certain weak solutions to the eikonal equations.

关键词： Lorentzian 2-torus weak solution class B metric