Asymptotic Behavior of the Compressible Navier-Stokes-Poisson Equations
-
摘要: 研究了等离子体物理科学中的三维可压Navier-Stokes-Poisson方程初边值问题解的整体存在性与长时间渐近性, 使用精细的能量估计证明了当初值是稳态解的小扰动时该问题存在唯一整体光滑解, 而且当t→∞时该整体光滑解以指数速率趋于稳态解.
-
关键词:
- 等离子体物理 /
- 可压Navier-Stokes-Poisson方程 /
- 渐近行为
Abstract: The authors studied the large time asymptotical behaviors of the smooth solutions to the initial boundary value problems for the three dimensional compressible Navier-Stokes-Poisson equations in plasma physics.By using the classical energy methods, it is proved that there exists a unique global and smooth solution to the initial-boundary value problems for the 3D compressible Navier-Stokes-Poisson equations which converges to a stationary solution exponentially fast as t→∞ when the initial data is near its equilibrium. -
-
[1] WANG Shu. Qusineutral limit of Euler-Poisson system with and without viscosity[J]. Commun Part Diff Eqs, 2004, 29 (3/4) : 419-456.
[2] WANG Shu, JIANG Song. The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations[J]. Commun Part Diff Eqs, 2006, 31 (4/6) : 571-591.
[3] BESSE C, CLAUDEL J, DEGOND P, et al. A model hierarchy for ionospheric plasma modelling[J]. M3AS, 2004, 14 (3) : 393-415.
[4] HAO Cheng-chun, LI Hai-liang. Global existence for compressible Navier-Stokes-Poisson equations in three and higher dimensions[J]. J Differential Equations, 2009, 246 (12) : 4791-4812.
[5] DONATELLI D. Local and global existence for the coupled Navier-Stokes-Poisson problem[J]. Quart Appl Math, 2003, 61 (2) : 345-361.
[6] YIN Jun-ping, TAN Zhong. Local existence of the strong solutions for the full Navier-Stokes-Poisson equations[J]. Nonlinear Analysis, 2009, 71 (7/8) : 2397-2415.
[7] DEGOND P, DELUZET F, SANGAM A, et al. An asymptotic preserving scheme for the Euler equations in a strong magnetic field[J]. Journal of Computational Physics, 2009, 228 (10) : 3540-3558.
[8] JU Qiang-chang, LI Fu-cai, LI Hai-liang. The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data[J]. J Differential Equations, 2009, 247 (1) : 203-224.
[9] DUCOMET B, FEIREISL E, PETZELTOVA H, et al. Global in time weak solution for compressible barotropic self-gravitating fluids[J]. Discrete Contin Dyn Syst, 2004, 11 (1) : 113-130.
[10] DUCOMET B, ZLOTNIK A. Stabilization and stability for the spherically symmetric Navier-Stokes-Poisson system[J]. Appl Math Lett, 2005, 18 (10) : 1190-1198.
[11] GUO Yan, WALTER S. Stability of semiconductor states with insulating and contact boundary conditions[J]. Arch Rational Mech Anal, 2006, 179 (1) : 1-30.
[12] HSIAO L, MARKOWICH P A, WANG Shu. The asymptotic behavior of globally smooth solutions of the multidimensional hydrodynamic model for semiconductors[J]. J Differential Equations, 2003, 192 (1) : 111-133.
计量
- 文章访问数: 22
- HTML全文浏览量: 0
- PDF下载量: 13
下载:
