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We construct a stable right inverse for the divergence operator innon-cylindrical domains in space-time. The domains are assumed to be H\"olderregular in space and evolve continuously in time. The inverse operator is ofBogovskij type, meaning that it attains zero boundary values. We provideestimates in Sobolev spaces of positive and negative order with respect to bothtime and space variables. The regularity estimates on the operator depend onthe assumed H\"older regularity of the domain. The results can naturally beconnected to the known theory for Lipschitz domains. As an application, weprove refined pressure estimates for weak and very weak solutions toNavier--Stokes equations in time dependent domains.

Construction of a right inverse for the divergence in non-cylindrical time dependent domains