# Inviscid limit for the axisymmetric stratified Navier–Stokes system

### Samira Sulaiman

Université de Rennes I, France

## 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 $(v_\nu,\rho_\nu)$ for this system with axisymmetric initial data belonging to the Sobolev space $H^{s}\times H^{s-2}$ with $s>{5}/{2}.$ 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 $(v_\nu, \rho_\nu)_{\nu>0}$ converge strongly in the space $L^{\infty}_{\text{loc}}(\mathbb{R}_+; H^{s}\times H^{s-2})$ to the solution $(v,\rho)$ 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