Abstract

The current paper deals with the local well-posedness problem for the two-dimensional partial viscous Boussinesq system when the initial vorticity belongs to the patch class. We prove in particular some results concerning the regularity persistence of the patch boundary and establish the convergence towards the inviscid limit when the molecular diffusivity goes to zero.

Keywords: Stratified system; vortex patches; local well-posedness; inviscid limit.

MSC: 35B65, 35Q35, 76D05

Pages:  285$-$303     

Volume  71 ,  Issue  4 ,  2019