Optimal rate of convergence in Stratified Boussinesq system

2017/02/17 by Zerguine, Mohamed, Meddour, Halima
#35B65 #35Q35 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.05302

Abstract

We study the vortex patch problem for 2d-stratified Navier-Stokes system. We aim at extending several results obtained in \citead,danchinpoche,hmidipoche for standard Euler and Navier-Stokes systems. We shall deal with smooth initial patches and establish global strong estimates uniformly with respect to the viscosity in the spirit of \citeHZ-poche, Z-poche. This allows to prove the convergence of the viscous solutions towards the inviscid one. In the setting of a Rankine vortex, we show that the rate of convergence for the vortices is optimal in L^p space and is given by (μt)^(1)/(2p). This generalizes the result of \citead obtained for L² space.

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