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global well-posedness of the BCL System with Viscosity

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Chinese Annals of Mathematics,Series B 2009年第2期30卷 153-172页

作者： Junqi HU Department of Applied Mathematics Shanghai University of Finance and Economics Shanghai 200433 China

The BCL system, a kind of equations governing the motion of the free surface of water waves in R3, is studied. Some results on the global existence, uniqueness and regularity of solutions to such system with small ini... 详细信息

关键词： Pseudo-differential operator Water waves global well-posedness

global well-posedness for 2D inhomogeneous asymmetric fluids with large initial data

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Science China Mathematics 2024年第3期67卷 527-556页

作者： Chenyin Qian Beibei He Ting Zhang School of Mathematical Sciences Zhejiang Normal UniversityJinhua 321004China School of Mathematical Sciences Zhejiang UniversityHangzhou 310058China

In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2D inhomogeneous incompressible asymmetric fluids with the initial(angular) velocity being located in sub-critical Sobolev spaces H^(s)(R^(2))(0global unique solvability of the 2D incompressible inhomogeneous asymmetric fluids with the initial data in the critical Besov space(u_(0), w_(0))∈˙B^(0)_(2,1)(R^(2))andρ^(−1)−1∈˙B^(ε)_(2/ε),1(R^(2))is established. In particular, the uniqueness of the solution is also obtained without any more regularity assumptions on the initial density which is an improvement on the recent result of Abidi and Gui(2021) for the 2D inhomogeneous incompressible NavierStokes system.

关键词： inhomogeneous asymmetric fluids Littlewood-Paley theory Besov spaces global well-posedness

global well-posedness and Scattering for the Defocusing H^s-Critical NLS

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Chinese Annals of Mathematics,Series B 2013年第6期34卷 801-842页

作者： Jian XIE Daoyuan FANG Department of Mathematics Hangzhou Normal University Department of Mathematics Zhejiang University

The authors consider the scattering phenomena of the defocusing H^s-critical *** is shown that if a solution of the defocusing NLS remains bounded in the critical homogeneous Sobolev norm on its maximal interval of ex... 详细信息

关键词： Nonlinear SchrSdinger equation Scattering global well-posedness

global well-posedness AND SCATTERING FOR THE MASS-CRITICAL HARTREE EQUATION IN HIGH DIMENSIONS

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Acta Mathematica Scientia 2015年第1期35卷 255-274页

作者：夏红强 College of Mathematics and Computer Science Wuhan Textile University

We obtain global well-posedness and scattering, and global L2（d＋2）/d t,x spacetime bounds for solutions to the defocusing mass-critical Hartree equation in Rt×Rx^d,d≥5.

关键词： Haxtree equation global well-posedness scattering mass-critical

global well-posedness IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION

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Acta Mathematica Scientia 2016年第4期36卷 1117-1152页

作者：霍朝辉 Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences

The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space is considered. It is shown that it is globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 if small initial data （u0 （x）, u1 （x）, n0 （x）, n1 （x）） ∈ （H^1 ×L^2× L^2 × H^-1）. It answers an open problem： Is it globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 for 3D Klein-Gordon- Zakharov 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^3 in one dimension [3] to higher dimension.

关键词： global well-posedness 3D Klein-Gordon-Zakharov equation dyadic Xs,b spacesin higher dimension

global well-posedness for the 2D Micropolar Rayleigh–Bénard Convection Problem without Velocity Dissipation

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Acta Mathematica Sinica,English Series 2021年第7期37卷 1053-1065页

作者： Sheng WANG Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433P.R.China

In this article,we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two *** first prove the local well-posedness of a smooth solution,and then establish a blow up criterion in terms of the gradient of scalar temperature *** last,we obtain the global well-posedness to the system.

关键词： 2D micropolar Rayleigh–Bénard convection problem blow-up criterion smooth solution global well-posedness

global well-posedness FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

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Acta Mathematica Scientia 2021年第1期41卷 164-176页

作者： Muhammad Zainul ABIDIN Jiecheng CHEN College of Mathematics and Computer Science Zhejiang Normal UniversityJinhua 321004China

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^(s(·))p(·),h(·),q(R^(3))with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^(4-2α-3/p(·))p(·),h(·)q(R^(3)).The result of this paper extends some recent work.

关键词： fractional Navier-Stokes equations global well-posedness Fourier-Besov-Morrey space

global well-posedness and global Attractor for Two-dimensional Zakharov-Kuznetsov Equation

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Acta Mathematica Sinica,English Series 2020年第9期36卷 969-1000页

作者： Min Jie SHAN Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China

The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in H^s(R^2)for all 5/7 详细信息

The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in H^s(R^2)for all 5/7global attractor for the weakly damped,forced Zakharov-Kuznetsov equation is also established in H^s(R^2)for10/11

关键词： Zakharov-Kuznetsov equation global well-posedness global attractor I-method atomic spaces

global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains

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Science China Mathematics 2021年第6期64卷 1231-1244页

作者： Kexin Li Boqiang Lü Yixuan Wang School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China College of Mathematics and Information Science Nanchang Hangkong UniversityNanchang 330063China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We consider the Cauchy problem for one-dimensional(1D)barotropic compressible Navier-Stokes equations with density-depending viscosity and large external *** a general assumption on the densitydepending viscosity,we prove that the Cauchy problem admits a unique global strong(classical)solution for the large initial data with ***,the density is proved to be bounded from above *** a consequence,we obtain the large time behavior of the solution without external forces.

关键词： 1D compressible Navier-Stokes equations global well-posedness large initial data vacuum density-depending viscosity