Lagrangian structure for compressible flow in the half-space with Navier boundary condition

Abstract

We show the uniqueness of particle paths of a velocity field, which solves the compressible isentropic Navier-Stokes equations in the half-space ℝ³₊ with the Navier boundary condition. More precisely, by energy estimates and the assumption of small energy we prove that the velocity field satisfies regularity estimates which imply the uniqueness of particle paths.