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

Abstract

We prove the global well-posedness of the two-dimensional Boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data [ $u_0\in L^2$, $\text{curl}{u}_0\in L^{\infty }$ and ${\theta }_0\in B_{q,p}^{2-2/p}$ with $p\in (1,\infty )$, $q\in (2,\infty )$ ]. Our method is based on the maximal regularity for heat equation.

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References in corpus (2)

• Global Regularity and Long-time Behavior of the Solutions to the 2D Boussinesq Equations without Diffusivity in a Bounded Domain
• Global Regularity for the Two-dimensional Boussinesq Equations Without Diffusivity in Bounded Domains