Construction of a Right Inverse for the Divergence in Non-cylindrical Time Dependent Domains

Abstract We construct a stable right inverse for the divergence operator in non-cylindrical domains space-time. The are assumed to be Hölder regular space and evolve continuously time. is of Bogovskij type, meaning that it attains zero boundary values. provide estimates Sobolev spaces positive negative order with respect both time variables. regularity on depend domain. results can naturally connected known theory Lipschitz domains. most precise given weighted spaces, where weight depends distance boundary. This allows deficit captured precisely vicinity irregularities As an application, we prove refined pressure weak very solutions Navier–Stokes equations dependent