Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D - Archive ouverte HAL Access content directly
Journal Articles Mathematical News / Mathematische Nachrichten Year : 2018

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

Abstract

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.
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Dates and versions

hal-01082319 , version 1 (13-11-2014)
hal-01082319 , version 2 (30-03-2018)

Identifiers

  • HAL Id : hal-01082319 , version 1

Cite

Boris Haspot. Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D. Mathematical News / Mathematische Nachrichten, In press. ⟨hal-01082319v1⟩
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