JournalsrmiVol. 30, No. 2pp. 431–462

Inviscid limit for the axisymmetric stratified Navier–Stokes system

  • Samira Sulaiman

    Université de Rennes I, France
Inviscid limit for the axisymmetric stratified Navier–Stokes system cover
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Abstract

This paper is devoted to the study of the Cauchy problem for the stratified Navier–Stokes system in three-dimensional space. In the first part of the paper, we prove the existence of a unique global solution (vν,ρν)(v_\nu,\rho_\nu) for this system with axisymmetric initial data belonging to the Sobolev space Hs×Hs2H^{s}\times H^{s-2} with s>5/2.s>{5}/{2}. The bounds on the solution are uniform with respect to the viscosity. In the second part, we analyse the inviscid limit problem. We prove that the viscous solutions (vν,ρν)ν>0(v_\nu, \rho_\nu)_{\nu>0} converge strongly in the space Lloc(R+;Hs×Hs2)L^{\infty}_{\text{loc}}(\mathbb{R}_+; H^{s}\times H^{s-2}) to the solution (v,ρ)(v,\rho) of the stratified Euler system.

Cite this article

Samira Sulaiman, Inviscid limit for the axisymmetric stratified Navier–Stokes system. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 431–462

DOI 10.4171/RMI/788