Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 106, pp. 1-26.

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

Authors: Marcelo M. Santos (Univ. Estadual de Campinas, SP, Brazil)
         Edson J. Teixeira (Univ. Federal de Vicosa, MG, Brazil)

Abstract:
 We show the uniqueness of particle paths of a velocity field, which solves the
 compressible isentropic Navier-Stokes equations in the half-space
 $\mathbb{R}_+^3$ 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.

Submitted March 5, 2019. Published September 18, 2019.
Math Subject Classifications: 35Q30, 76N10, 35Q35, 35B99.
Key Words: Navier-Stokes equations; Lagrangian structure; Navier boundary condition.