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