Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D

Haspot, Boris

Haspot, Boris (2018), Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D, Mathematische Nachrichten, 291, 14-15, p. 2188-2203. 10.1002/mana.201700050

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1411.5503v2

Date

2018

Journal name

Mathematische Nachrichten

Volume

291

Number

14-15

Publisher

Wiley

Pages

2188-2203

Abstract (EN)

We consider Navier-Stokes equations for compressible viscous fluids in one dimen-sion. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new formulation of the compressible equations involving a new effective velocity v (see [8, 11, 10, 9]) such that the density verifies a parabolic equation. We estimate v in L ∞ norm which enables us to control the vacuum on the density.

Subjects / Keywords

Navier-Stokes equations; degenerate viscosity coefficients