On the \(\delta\)-primitive and Boussinesq type equations (Q2504046)

The authors consider the so-called \(\delta\)-primitive equations without horizontal viscosity but with a mild vertical viscosity added in the hydrostatic equation. They also consider a Boussinesq type of equations in which mild vertical viscosity in the hydrostatic equation is replaced by the time derivatiye of the vertical velocity. For both types of equations, the authors prove the finite-in-time existence, uniqueness and continuous dependence on data for appropriate solutions. The proofs are based on Galerkin-Fourier method, where approximate solutions are the solutions of a finite-dimensional equation with bilinear nonlinearity.