An elementary approach to the inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations
type: Item
instance of: scholarly article
title: An elementary approach to the inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations
zbMATH Open document ID: 1304.35480
author: Luigi C. Berselli
author: Stefano Spirito
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.6882
review text: The authors prove that the weak solution \(u_{\nu}\) of the 3D Navier-Stokes equations converges in \(L^{\infty}(0,T;L^2(\Omega))\) to the solution of the corresponding Euler equations, as \(\nu \) tends to zero. The rate of converges strongly depends on the initial data. These facts are then used to show that the solution \((u_{\nu}, \rho_{\nu})\) of the 3D Boussinesq equations (without diffusion, with Navier type slip boundary conditions) approaches the solution of the Euler-Boussinesq equations.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 6358117
zbMATH Keywords: 3D Boussinesq equations
zbMATH Keywords: 3D Navier-Stokes equations
zbMATH Keywords: Navier type slip boundary conditions
zbMATH Keywords: vanishing viscosity limits
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
OpenAlex ID: W1996309486
arXiv ID: 1207.6882
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DOI: 10.1007/S00030-013-0242-1
description: scientific article; zbMATH DE number 6358117