...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >The inviscid limit of the incompressible anisotropic Navier-Stokes equations with the non-slip boundary condition
【24h】

The inviscid limit of the incompressible anisotropic Navier-Stokes equations with the non-slip boundary condition

机译：具有防滑边界条件的不可压缩各向异性Navier-Stokes方程的无粘性极限

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

In this paper, we study the asymptotic behavior for the incompressible anisotropic Navier-Stokes equations with the non-slip boundary condition in a half space of R3 when the vertical viscosity goes to zero. Firstly, by multi-scale analysis, we formally deduce an asymptotic expansion of the solution to the problem with respect to the vertical viscosity, which shows that the boundary layer appears in the tangential velocity field and satisfies a nonlinear parabolic-elliptic coupled system. Also from the expansion, it is observed that away from the boundary the solution of the anisotropic Navier-Stokes equations formally converges to a solution of a degenerate incompressible Navier-Stokes equation. Secondly, we study the well-posedness of the problems for the boundary layer equations and then rigorously justify the asymptotic expansion by using the energy method. We obtain the convergence results of the vanishing vertical viscosity limit, that is, the solution to the incompressible anisotropic Navier-Stokes equations tends to the solution to degenerate incompressible Navier-Stokes equations away from the boundary, while near the boundary, it tends to the boundary layer profile, in both the energy space and the L ∞ space.
机译：在本文中，我们研究了当垂直粘度为零时，在R3半空间中具有防滑边界条件的不可压缩各向异性Navier-Stokes方程的渐近行为。首先，通过多尺度分析，我们就垂直粘度正式推导了该问题的解的渐近展开，这表明边界层出现在切向速度场中，并且满足非线性抛物线-椭圆耦合系统。同样从扩展中可以看出，各向异性的Navier-Stokes方程的解远离边界而正式收敛到退化的不可压缩Navier-Stokes方程的解。其次，我们研究了边界层方程问题的适定性，然后使用能量方法严格证明了渐近展开的合理性。我们获得了消失的垂直粘度极限的收敛结果，也就是说，不可压缩的各向异性Navier-Stokes方程的解趋于使不可压缩的Navier-Stokes方程远离边界退化，而在边界附近，则趋向于在能量空间和L∞空间中的边界层轮廓。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号