4 problems

The primitive equations are considered with fractional horizontal dissipation exponent $\alpha$, and the currently established global well-posedness result for general initial data…

For modes indexed by $n$, let $n_c$ satisfy … with the non-generic integer case excluded. For subcritical modes $1\leq n<n_c$, impose … … For supercritical modes $n>n_c$, impose ……

Let $u_0$ and $v_0$ denote the boundary traces of the velocity components in the zero-mode system, and impose … … The corresponding linearized system is known to be well posed. Fin…

The inviscid primitive equations (PEs) are considered in a limited domain with proposed nonlocal boundary conditions. Numerical simulations of the corresponding nonlinear equations…