# Lagrangian Structure for Compressible Flow in the Half-space with the Navier Boundary Condition.

@article{Santos2018LagrangianSF, title={Lagrangian Structure for Compressible Flow in the Half-space with the Navier Boundary Condition.}, author={Marcelo M. Santos and Edson J. Teixeira}, journal={arXiv: Analysis of PDEs}, year={2018} }

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. In particular, by means of energy estimates and the assumption of small energy we prove that the velocity field satisfies the necessary regularity needed to prove the uniqueness of particle paths.

#### One Citation

Lagrangian structure for two dimensional non-barotropic compressible fluids

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We study the lagrangian structure for weak solutions of two dimensional Navier-Stokes equations for a non-barotropic compressible fluid, i.e. we show the uniqueness of particle trajectories for two… Expand

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