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Boltzman方程及其相关宏观模型
  • 项目名称：Boltzman方程及其相关宏观模型
  • 项目类别：重点项目
  • 批准号：10431060
  • 申请代码：A0108
  • 项目来源：国家自然科学基金
  • 研究期限：2005-01-01-2008-12-31
  • 项目负责人：肖玲
  • 负责人职称：研究员
  • 依托单位：中国科学院数学与系统科学研究院
  • 批准年度：2004
中文摘要：

本项目研究Boltzmann方程及其相关宏观模型，包括经典与量子Boltzmann方程的基本问题，Boltzmann方程与Navier-Stokes 方程的非线性波现象，Boltzmann-Poisson方程与相关宏观模型的数学理论，特别是流体动力学极限问题以及各种流体力学模型之间的渐近机制，Quantum Euler-Poisson方程与其它量子修正宏观模型的适定性及各种渐近极限问题，不可压Euler方程弱解的整体存在性、解的奇异性分析和逼近解序列的强收敛，不可压Navier-Stokes方程整体强解存在唯一性和弱解的正则性理论，可压Euler方程和Navier-Stokes方程的真空问题，具耗散机制拟线性双曲组整体解的渐近行为，等。以上研究内容不仅是国际上十分重视的、具有前沿性和主流兴趣的、有重要理论意义，而且是紧密联系应用科学和工程技术的、有广泛的应用前景。

中文主题词： Boltzmann方程;Navier-Stokes 方程;Euler方程;Quantum Hydrod
成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 99
  • 3
  • 0
  • 0
  • 0
期刊论文
Nonlinear stability of rarefaction waves for the Boltzmann equation
A case study of global stability of strong rarefaction waves for 2×2 hyperbolic conservation laws wi
Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system
Optimal (1) decay rates to linear diffusion waves for nonlinear evolution equations with elliptici
On the Strong Convergence to 3D Steady Vortex Sheets
Spherically Symmetric Isentropic Compressible Flows with Density-Dependent Viscosity Coefficients
and BV-type Stability of the Boltzmann Equation with External Forces
Convergence to diffusion waves for nonlinear evolution equations with ellipticity and damping, and w
Quasineutral limit of a time-dependent drift-diffusion-Poisson models for p-n junction semiconductor
Study on a cross diffusion parabolic system
Partial regularity of suitable weak solutions to incompressible magneto-hydrodynamic equations
Nonstationary Navier-Stokes flows in a two-dimensional exterior domain with rotational symmetries.
Algebraic time decay for the bipolar quantum hydrodynamic model
Global well posedness for the Gross- Pitaevskii equation with an angular momentum rotational term
Dissipation and dispersion approximation to hydrodynamical equations and asymptotic limit
On the Regularity Criteria for Weak Solutions to the Magnetohydrodynamic Equation
Remark on the regularity for weak solutions to the Magnetohydrodynamic equations
Remark On the Spatial Partial Regularity for the Navier-Stokes Equations
Moment Estimates for Weak Solutions to the Navier-Stokes Equations in Half-Space
On weighted norm estimates for solutions to nonstationary incompressible Navier-Stokes equations in
On two-dimensional Navier- Stokes flows with rotational symmetries
On Strong Convergence to 3-D Axisymmetric Vortex Sheets
Vanishing of vacuum and blow-up phenomena of the compressible Navier-Stokes equations
Behaviour of the Fokker-Planck- Boltzmann equation near a Maxwellian
Boussinesq方程解的部分正则性
Mathematical Results Related to A Two-Dimensional Magneto-hydrodynamic Equations
Global upper and lower bounds on solutions to drift-diffusion semiconductor equations (Chinese)
Convergence rate to stationary solutions for Boltzmann equation with external force
Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stok
Vanishing Viscous Limits for the 2D Lake Equations with Navier Boundary Conditions
Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation
Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semicondu
Global solutions to 1D compressible Navier-Stokes-Poisson equations with density-dependent viscosit
Convergence of the Vlasov-Poisson- Boltzmann system to the incompressible Euler equations
stability for the Vlasov-Poisson-Boltzmann system around vacuum
Asymptotics in nonlinear evolution system with dissipation and ellipticity on quadrant
Stationary solutions to Euler equations with spherical symmetry
Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum
Cauchy problem for the Vlasov- Poisson-Boltzmann system
Wellposedness of Cauchy problem for the fourth order nonlinear Schr?dinger equations in multi-dimens
Quasi-neutral limit of the drift- diffusion model for semiconductors with general sign-changing dopi
Global solutions of the Boltzmann equation with external forces
Asymptotic stability of the Relativistic Maxwellian
Combined quasineutral and inviscid limit of the Vlasov-Poisson-Fokker- Planck system
Decay rates to the planar rarefaction waves for a model system of the radiating gas in n-dimensions
Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption
Convergence rate for the compressible Navier-Stokes equations with external force
Global existence and asymptotics of solutions of the Cahn-Hilliard equation
Optimal convergence rates for the compressible Navier-Stokes equations with potential forces
Convergence rates of solutions toward boundary layer solutions for generalized Benjamin-Bona-Mahony-
The Cauchy Problem for 1D Compressible Flows with Density- Dependent Viscosity Coefficients
Navier-Stokes Approximations to 2D Vortex Sheets in Half Plane,
Studies on Schr?dinger-Poisson systems (Excerpt of Dissertation)
Asymptotics toward strong nonlinear rarefaction waves for systems of 2×2 viscous conservation laws
Wellposedness for the fourth order nonlinear Schr?dinger equations
The relaxation-time limit in the quantum hydrodynamic equations for semiconductors
Zero Debye length asymptotic of the quantum hydrodynamic model for semiconductors
Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping
Global existence to Boltzmann equation with external force in infinite vacuum
Asymptotics of dissipative nonlinear evolution equations with ellipticity: different end states
Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant
Decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity
Vacuum problem for 1D compressible Navier-Stokes equations with gravity and general pressure law
Nonlinear stability of rarefaction waves for the compressible Navier-Stokes equations with large ini
Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence
Decay rates toward stationary waves of solutions for damped wave equations
Global Existence for compressible Navier-Stokes-Poissonequations in three and higher dimensions
Long-time self-similar asymptotic of the macroscopic quantum models
Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors
Large time behavior and relaxation energy limit of the solutions to a multi-dimensional energy trans
Large-time behavior of solutions of quantum hydrodynamic model for semiconductors
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption
A new energy method for the Boltzmann equation
Existence and non-existence of time-global solutions to damped wave equation on half-line
Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system
Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their ap
decay rates of planar viscous rarefaction wave for scalar conservation law with degenerate viscosity
Weak and Strong Solutions for the Incompressible Navier-Stokes Equations with Damping Term
Global classical solution to the initial value problem for the relativistic Landau equation
A half-space problem for the Boltzmann equation with specular reflection boundary condition
Existence of global smooth solution to the relativistic Euler equations
Global stability of strong rarefaction waves for the generalized Kdv-Burgers equation
Diffusive property of the Fokker-Planck-Boltzmann equation
DECAY RATES TOWARD STATIONARY WAVES OF SOLUTIONS FOR DAMPED WAVE EQUATIONS
Vlasov-Maxwell-F0kker-Planck方程组的极限问题
一类四阶抛物型方程的解的渐近行为
求解随机微分方程的两种方法的稳定性分析
具有退化粘性的非齐次双曲守恒律方程的Cauchy问题
Boussinesq方程组解的正则类
ASYMPTOTIC DECAY TOWARD RAREFACTION WAVE FOR A HYPERBOLIC-ELLIPTIC COUPLED SYSTEM ON HALF SPACE
会议论文
Global existence of solutions to a hyperbolic-parabolic system
Existence of strong traveling wave profiles to 22 system of viscous conservation laws
A note on global smooth solution to the p-system with damping
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