Optimal rate of convergence in Stratified Boussinesq system
Zerguine, Mohamed · Meddour, Halima
Original · EN
We study the vortex patch problem for 2d-stratified Navier-Stokes system. We aim at extending several results obtained in ad,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 HZ-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 Lᵖ space and is given by (μt)¹/²ᵖ. This generalizes the result of ad obtained for L² space.
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