Electron. J. Differential Equations, Vol. 2019 (2019), No. 106, pp. 1-26.

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

Marcelo M. Santos, Edson J. Teixeira

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.

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  Marcelo M. Santos
Departamento de Matemática, IMECC-UNICAMP
Universidade Estadual de Campinas
Rua Sérgio Buarque de Holanda, 651
13083-859 - Campinas - SP, Brazil
email: msantos@ime.unicamp.br
Edson J. Teixeira
Departamento de Matemática
UFV (Universidade Federal de Viçosa)
Av. PH. Rolfs, s/n, 36570-900 - Viçosa - MG, Brazil
email: edson.teixeira@ufv.br

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