Inviscid limit for vortex patches in a bounded domain

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• 作者：Quansen Jiu ; Yun Wang
• 关键词：Inviscid limit ; Navier boundary condition ; Vortex patches
• 刊名：Applied Mathematics Letters
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：25
• 期：10
• 页码：1367-1372
• 全文大小：221 K

文摘

In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain . We prove that for a vortex patch initial data, the weak Leray solutions of the incompressible Navier-Stokes equations with Navier boundary conditions will converge (locally in time for and globally in time for ) to a vortex patch solution of the incompressible Euler equation as the viscosity vanishes. In view of the results obtained in Abidi and Danchin (2004)? and Masmoudi (2007)? which dealt with the case of the whole space, we derive an almost optimal convergence rate for any small in .