Inviscid limit for the two-dimensional Navier-Stokes system in a critical Besov space

Taoufik Hmidi; Sahbi Keraani

Inviscid limit for the two-dimensional Navier-Stokes system in a critical Besov space

Taoufik Hmidi, Sahbi Keraani

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In a recent paper (Arch. Rational Mech. Anal. 145(3) (1998), 197-214), Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B_2,1 ². In the present paper we prove that the Navier-Stokes system is globally well-posed in B _2,1 ², with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L² is of order ν.

Original language	English (US)
Pages (from-to)	125-138
Number of pages	14
Journal	Asymptotic Analysis
Volume	53
Issue number	3
State	Published - 2007

Keywords

Inviscid limit
Navier-Stokes and Euler equations
Vorticity flows

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "In a recent paper (Arch. Rational Mech. Anal. 145(3) (1998), 197-214), Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B2,1 2. In the present paper we prove that the Navier-Stokes system is globally well-posed in B 2,1 2, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L2 is of order ν.",

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AU - Keraani, Sahbi

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AB - In a recent paper (Arch. Rational Mech. Anal. 145(3) (1998), 197-214), Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B2,1 2. In the present paper we prove that the Navier-Stokes system is globally well-posed in B 2,1 2, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L2 is of order ν.

KW - Inviscid limit

KW - Navier-Stokes and Euler equations

KW - Vorticity flows

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ER -

Inviscid limit for the two-dimensional Navier-Stokes system in a critical Besov space

Abstract

Keywords

ASJC Scopus subject areas

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