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 Bpq2/pβ for p,qβ(1,β) with
1/p+1/qβ€1. This solution regularize instantaneously and becomes even
real analytic for t>0.Comment: 19 page