Differential and Integral Equations

Inviscid limit for axisymmetric Navier-Stokes system

Taoufik Hmidi and Mohamed Zerguine

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Abstract

We are interested in the global well posedness of the axisymmetric Navier-Stokes system with initial data belonging to the critical Besov spaces ${B}_{p, 1}^{1+\frac{3}{p}}$. We obtain uniform estimates of the viscous solutions $(v_\nu)$ with respect to the viscosity in the spirit of the work [2] concerning the axisymmetric Euler equations. We provide also a strong convergence result in the $L^p$ norm of the viscous solutions $(v_\nu)$ to the Eulerian one $v$.

Article information

Source
Differential Integral Equations Volume 22, Number 11/12 (2009), 1223-1246.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019414

Mathematical Reviews number (MathSciNet)
MR2555646

Zentralblatt MATH identifier
1228.76037

Subjects
Primary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Hmidi, Taoufik; Zerguine, Mohamed. Inviscid limit for axisymmetric Navier-Stokes system. Differential Integral Equations 22 (2009), no. 11/12, 1223--1246. https://projecteuclid.org/euclid.die/1356019414.


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