Gevrey solutions of quasi-linear hyperbolic hydrostatic Navier-Stokes system

时   间：  2023-04-16 19:00 — 21:00

We study the well-posednessof  a hyperbolic quasilinear version of hydrostatic  Navier-Stokes system in  $\R\times\T$, and  prove the global well-posedness of the system with initial  data which are small and analytic  in both variables. We also prove the convergence of such analytic solutions to that of the classical hydrostatic Navier-Stokes system when the delay time converges to zero. Furthermore, we obtain a local well-posednessresult in Gevrey class $2$ when the initial datum is a small perturbation of some convex function.