Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
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Rate of Convergence in Inviscid Limit for 2D Navier-Stokes Equations with Navier Fricition Condition for Nonsmooth Initial Data

  • Kim, Namkwon (Department of Mathematics, Chosun University)
  • Received : 2013.02.27
  • Accepted : 2013.03.25
  • Published : 2013.03.30
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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($u{\in}W^{2,p}$, 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.

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References

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