Analyticity of solutions to the primitive equations

Abstract

This article presents the maximal regularity approach to the primitive equations. It is proved that the $3D$ primitive equations on cylindrical domains admit a unique, global strong solution for initial data lying in the critical solonoidal Besov space $B_{pq}^{2/p}$ for $p,q\in (1,\infty )$ with $1/p+1/q\le 1$. This solution regularize instantaneously and becomes even real analytic for $t>0$.

19 pages