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

Abstract

AbstractIn 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 $p(x,y,t)$ p ( x , y , t ) is a concave function. We also consider the equations on the line $x=0$ x = 0 , $y=0$ y = 0 .