On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
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DOI：
10.1088/0951-7715/11/6/011
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发表时间：
1998
期刊：
影响因子：
1.7
通讯作者：
Thierry Clopeau;Andro Mikelic;Raoul Robert
中科院分区：
文献类型：
--
作者：
Thierry Clopeau;Andro Mikelic;Raoul Robert
研究了有界区域上二维不可压Navier-Stokes方程的粘性消失极限。受湍流研究的启发，我们假设切向方向的Navier摩擦条件，即产生与切向速度成比例的涡量。本文证明了具有光滑相容数据的Navier-Stokes方程正则解的存在性，以及当初始涡量仅有界时，有界涡量解的存在性。最后，在无粘极限下，我们建立了涡量的一个一致界，并证明了其收敛性。
The vanishing viscosity limit is considered for the incompressible 2D Navier-Stokes equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's friction condition in the tangential direction, i.e. the creation of a vorticity proportional to the tangential velocity. We prove the existence of the regular solutions for the Navier-Stokes equations with smooth compatible data and of the solutions with bounded vorticity for initial vorticity being only bounded. Finally, we establish a uniform -bound for the vorticity and convergence to the incompressible 2D Euler equations in the inviscid limit.