Martin Saal. Source: Advances in Differential Equations, Volume 25, Number 11/12, 651--685.Abstract:
We consider the $3D$ primitive equations and show, that one does need less than horizontal viscosity to obtain a well-posedness result in Sobolev spaces. Furthermore, we will also investigate the primitive equations with horizontal viscosity and show that these equations are well-posed without imposing any boundary condition for the horizontal velocity components on the vertical boundary.