Global Regularity for the Two-dimensional Boussinesq Equations Without Diffusivity in Bounded Domains

Abstract

We address the well-posedness for the two-dimensional Boussinesq equations with zero diffusivity in bounded domains. We prove global in time regularity for rough initial data: both the initial velocity and temperature have $\epsilon$ fractional derivatives in $L^q$ for some $q>2$ and $\epsilon >0$ arbitrarily small.

Minor revision

References in corpus (2)

• Global Regularity and Long-time Behavior of the Solutions to the 2D Boussinesq Equations without Diffusivity in a Bounded Domain
• The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity

Cited by in corpus (1)

• Global well-posedness for the 2D Boussinesq Equations with Zero Viscosity