Rate of Convergence in Inviscid Limit for 2D Navier-Stokes Equations with Navier Fricition Condition for Nonsmooth Initial Data

• Journal title : Journal of the Chosun Natural Science
• Volume 6, Issue 1,  2013, pp.53-56
• Publisher : The Research Institute of Chosun Natural Science
• DOI : 10.13160/ricns.2013.6.1.053
Title & Authors
Rate of Convergence in Inviscid Limit for 2D Navier-Stokes Equations with Navier Fricition Condition for Nonsmooth Initial Data
Kim, Namkwon;

Abstract
We are interested in the rate of convergence of solutions of 2D Navier-Stokes equations in a smooth bounded domain as the viscosity tends to zero under Navier friction condition. If the initial velocity is smooth enough($\small{u{\in}W^{2,p}}$, p>2), it is known that the rate of convergence is linearly propotional to the viscosity. Here, we consider the rate of convergence for nonsmooth velocity fields when the gradient of the corresponding solution of the Euler equations belongs to certain Orlicz spaces. As a corollary, if the initial vorticity is bounded and small enough, we obtain a sublinear rate of convergence.
Keywords
Navier-Stokes;Inviscid Limit;
Language
English
Cited by
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