Regularity criteria for the 3D tropical climate model in Morrey–Campanato space

Abstract

In this paper we investigate the regularity criterion for the local-in-time smooth solution to the three-dimensional (3D) tropical climate model in the Morrey--Campanato space. It is shown that if $u $ satisfies \[\int^{T}_{0}\frac{\|\nabla u(t)\|^{\frac{2}{r}}_{\dot{\mathcal{M}}_{2,3/r}}}{\ln(\|u(t)\|_{L^2}+e)}dt<\infty\quad \text{with}\ 0<r<1,\] then the smooth solution $(u,v, \theta)$ can be extended past time $T$.

Keywords

• tropical climate model
• regularity criterion
• morrey–campanato space