Yudovich type solution for the two dimensional Euler-Boussinesq system with critical dissipation and general source term

Abstract

The present article investigates the two-dimensional Euler-Boussinesq system with critical fractional dissipation and general source term. First, we show that this system admits a global solution of Yudovich type, and as a consequence, we treat the regular vortex patch issue.

Keywords

• boussinesq system
• weak solutions
• besov spaces
• fractional dissipation
• regular vortex patch