Finite-time blowup for the 2-D viscous primitive equations of ocean and atmosphere dynamic

The atmosphere and ocean primitive equation, which are consist of fluid equations, thermodynamic equations state play a important role for numerical weather precdiction.In an earlier work we have shown the finite-time blowup 3-D oceanic atmospheric dynamics without viscosity by using method self-similar solutions.In this paper show that certain class initial data, corresponding smooth solutions 2-D viscous blow up in finite time.Specifically, consider area subject to y-direction periodic boundary conditions x-direction.To overcome term, assume pressure function $ p(x, , y, t) be concave reduce into new on line x = 0 with conditions; then prove reduced system develop singularities time.