Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension - Archive ouverte HAL
Article Dans Une Revue Communications in Mathematical Sciences Année : 2017

Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension

Résumé

We prove weak-strong uniqueness results for the compressible Navier-Stokes sys-tem with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in [20] so that it is unique. The main novelty consists in dealing with initial density ρ 0 which contains vacuum, indeed the most of the results exclude this situation in order to use the parabolic-ity of the momentum equation (see [25]). To do this we use the notion of relative entropy developed recently by Germain and Feireisl et al (see [9, 8]) combined with a new formulation of the compressible system ([10, 12, 11, 13]), more precisely we introduce a new effective velocity which makes the system parabolic on the density and hyperbolic on this velocity.
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Dates et versions

hal-01084223 , version 1 (18-11-2014)

Identifiants

  • HAL Id : hal-01084223 , version 1

Citer

Boris Haspot. Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension. Communications in Mathematical Sciences, 2017, 15 (3), pp.587-591. ⟨hal-01084223⟩
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