The Euler Equations with Variable Coefficients

Abstract

Abstract. We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data [Formula: see text] under the optimal regularity condition [Formula: see text]. In the case [Formula: see text], we further prove a Beale–Kato–Majda-type criterion that relates blowup in the [Formula: see text] norm to the [Formula: see text] norm of the variable vorticity.