Local well-posedness to the vacuum free boundary problem of full compressible Navier-Stokes equations in R3

Abstract In this paper, we prove the local well-posedness of the free boundary problem of full compressible Navier-Stokes equations with physical vacuum in three dimensions. We establish a priori estimates in Conormal Sobolev spaces in Lagrangian coordinates, where only the first-order time-derivative of the velocity is involved in the compatibility condition. The existence and uniqueness results of local-in-time solutions are based on a fixed point argument. Different from the isentropic case [11] , the presence of nonlinear term div ( u S ) in energy equation causes more difficulties. Moreover, we deal with this free boundary problem starting from the general cases of 1 γ ≤ 2 (the most physically relevant regime), where γ is the adiabatic exponent.