Revista Matemática Iberoamericana

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Volume 30, Issue 2, 2014, pp. 431–462
DOI: 10.4171/RMI/788

Published online: 2014-07-08

Inviscid limit for the axisymmetric stratified Navier–Stokes system

Samira Sulaiman[1]

(1) Université de Rennes I, France

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.

Keywords: Navier–Stokes equations, paradifferential operators, incompressible viscous fluids, stratification effects in viscous fluids

Sulaiman Samira: Inviscid limit for the axisymmetric stratified Navier–Stokes system. Rev. Mat. Iberoam. 30 (2014), 431-462. doi: 10.4171/RMI/788