Communications in Mathematical Sciences

Volume 17 (2019)

Number 6

Inviscid limit for axisymmetric Navier–Stokes–Boussinesq system

Pages: 1625 – 1652

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n6.a6

Authors

Hammadi Abidi (Département de Mathématiques, Faculté des Sciences, Université de Tunis El Manar, Tunis, Tunisia)

Guilong Gui (Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi’an, China)

Abstract

Consideration herein is the inviscid limit of the 3D incompressible axisymmetric Navier–Stokes–Boussinesq system with partial viscosity. We obtain uniform estimates of the solutions of this system with respect to the viscosity. We then provide a strong convergence result in the $H^{s-2}$ norm of the viscous solutions of this Navier–Stokes–Boussinesq system to the one of Euler–Boussinesq equations.

Keywords

inviscid limit, Navier–Stokes–Boussinesq system, axisymmetric velocity

2010 Mathematics Subject Classification

76B03, 76D03, 76D09

Full Text (PDF format)

The work of Guilong Gui is supported in part by the National Natural Science Foundation of China under Grants 11571279 and 11331005.

Received 29 August 2018

Accepted 1 July 2019

Published 26 December 2019