Finite-time blowup for the 3-D viscous primitive equations of oceanic and atmospheric dynamics

In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function p(x,y,t) is a concave function. We also consider the equations on the line x=0 , y=0 .