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可压缩Navier-Stokes方程的一些研究
  • 项目名称：可压缩Navier-Stokes方程的一些研究
  • 项目类别：面上项目
  • 批准号：11171154
  • 申请代码：A010801
  • 项目来源：国家自然科学基金
  • 研究期限：2012-01-01-2015-12-31
  • 项目负责人：樊继山
  • 负责人职称：教授
  • 依托单位：南京林业大学
  • 批准年度：2011
中文摘要：

本项目拟研究可压缩Navier-Stokes方程。可压缩Navier-Stokes方程在应用上和理论上都是极其重要的一组偏微分方程，可压缩Navier-Stokes方程自从提出这一方程起已有近二百年的历史。可压缩Navier-Stokes方程的研究在理论上必将促进偏微分方程、泛函分析、调和分析、几何测度论、科学计算等数学分支的发展，在应用上对航海、航空、数值天气预报等高科技领域都将有至关重要的作用。可压缩Navier-Stokes方程分等熵Navier-Stokes方程和非等熵Navier-Stokes方程。本项目拟研究等熵Navier-Stokes方程的弱解的能量等式、非等熵Navier-Stokes方程在球外区域上的球对称弱解的唯一性及三维非等熵Navier-Stokes方程Cauchy问题的非平凡时间周期解的存在性。

中文主题词： Navier-Stokes；磁流体方程；超导方程；epitaxial growth models；正则性准则
英文摘要：

Navier-Stokes；MHD；superconductivity；epitaxial growth models；regularity criterion

英文主题词： Navier-Stokes；MHD；superconductivity；epitaxial growth models；regularity criterion
结论摘要：

本项目研究流体力学及相关方程的数学理论。流体力学方程在应用上和理论上都是极其重要的一组偏微分方程。流体力学方程的研究在理论上必将促进偏微分方程、泛函分析、调和分析、数学物理、几何测度论、随机分析等数学分支的发展；在应用上对气象学、空气动力学、热动力学、等离子体物理学、材料科学、计算流体力学等高科技领域都将有十分重要的作用。 本项目研究3维可压缩full Navier-Stokes方程、磁流体力学方程、可压缩等熵Navier-Stokes-Maxwell方程、2维广义磁流体力学方程、超导方程和epitaxial growth models。 本项目证明了3维可压缩 full Navier-Stokes 方程的强解当热传导系数 k=0 时的一个正则性准则；证明了3维磁流体力学方程组的一些正则性准则；证明了有界区域上的等熵 Navier-Stokes-Maxwell 方程组当马赫数或介电常数消失时的极限；证明了2维广义磁流体力学方程组古典解的存在唯一性；用流体力学方程中的方法，证明了3维超导方程组的弱解在临界空间中的唯一性；用流体力学方程中的方法证明了4维 epitaxial growth models 古典解的存在唯一性，从而解决了一个 open problem。

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期刊论文
A blow-up criterion of strong solutions to the compressible viscous heat-conductive flows with zero
A blow-up criterion for compressible nematic liquid crystal flows
Blow-up criteria for 3D nematic liquid crystal models in a bounded domain
A GRADIENT ESTIMATE FOR SOLUTIONS TO PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
The vanishing viscosity limit for a 2D Cahn-Hilliard-Navier-Stokes system with a slip boundary condi
Weak-strong uniqueness for the generalized Navier-Stokes equations
A regularity criterion to the biharmonic map heat flow in R-4
The vanishing viscosity limit for a 3D model of electro-kinetic fluid in a bounded domain
Blow up criterion for a hyperbolic-parabolic system arising from chemotaxis
Uniqueness of Weak Solutions to an Electrohydrodynamics Model
Uniform existence for a 3D time-dependent Ginzburg-Landau model in superconductivity
Global Cauchy problem of 2D generalized magnetohydrodynamic equations
Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations
Global Dynamics of a Coupled Chemotaxis-Fluid Model on Bounded Domains
UNIFORM LOCAL WELL-POSEDNESS AND REGULARITY CRITERION FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE FLOW
GLOBAL STRONG SOLUTION TO THE TWO-DIMENSIONAL DENSITY-DEPENDENT MAGNETOHYDRODYNAMIC EQUATIONS WITH V
Uniform existence of the 1-D full equations for a thermo-radiative electromagnetic fluid
Global Cauchy problem for a 2D magnetic Benard problem with zero thermal conductivity
On the Cauchy problem for a model of electro-kinetic fluid
Logarithmically improved regularity criteria for the 3D viscous MHD equations
Blow-Up Criteria of Smooth Solutions for the Cahn-Hilliard-Boussinesq System with Zero Viscosity in
Regularity criteria for the incompressible Hall-magnetohydrodynamic equations
Global cauchy problem of 2D generalized MHD equations
REGULARITY CRITERIA FOR THE 2D MHD SYSTEM WITH HORIZONTAL DISSIPATION AND HORIZONTAL MAGNETIC DIFFUS
Regularity criteria for the density-dependent Hall-magnetohydrodynamics
Regularity criteria for the three-dimensional magnetohydrodynamic equations
Global solutions to the Navier-Stokes-(omega)over-bar and related models with rough initial data
Global strong solution to the 2D density-dependent liquid crystal flows with vacuum
Time decay rate for two 3D magnetohydrodynamics- alpha models
Uniform existence of the 1-d complete equations for an electromagnetic fluid
Regularity criteria for the Euler-Landau-Lifshitz system
EXISTENCE OF SMOOTH GLOBAL SOLUTIONS FOR A 1-D MODIFIED NAVIER-STOKES-FOURIER MODEL
Global well-posedness for the 4D epitaxial growth models.
A BLOW-UP CRITERION FOR THE MHD EQUATIONS WITH MASS DIFFUSION
Uniform Local Well-Posedness to the Density-Dependent Navier-Stokes-Maxwell System
Regularity criteria and uniform estimates for the Boussinesq system with temperature-dependent visco
LOGARITHMICALLY IMPROVED REGULARITY CRITERIA FOR THE GENERALIZED NAVIER-STOKES AND RELATED EQUATIONS
Uniqueness of weak solutions to the 3D Ginzburg-Landau superconductivity model.
Laplace积分的一种新求法
Two regularity criteria for 3D Navier-Stokes equations in a bounded domain
Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bound
A regularity criterion for 3D micropolar fluid flows
Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity
A note on regularity criterion for the 3D Boussinesq system with zero thermal conductivity
Blow-up criteria of smooth solutions to the 3D Boussinesq system with zero viscosity in a bounded do
A regularity criterion for a fluid system with the linear Soret effect
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