New formulation of the compressible Navier-Stokes equations and parabolicity of the density
Haspot, Boris (2014), New formulation of the compressible Navier-Stokes equations and parabolicity of the density. https://basepub.dauphine.fr/handle/123456789/14365
TypeDocument de travail / Working paper
External document linkhttp://arxiv.org/pdf/1411.5501.pdf
MetadataShow full item record
Abstract (EN)In this paper we give a new formulation of the compressible Navier-St okes by introducing an suitable effective velocity v = u + ∇ φ ( ρ ) provided that the viscosity coefficients verify the algebraic relation of . We give in particular a ve ry simple proof of the entropy discovered in , in addition our argument show why the al- gebraic relation of  appears naturally. More precisely the system reads in a very surprising way as two parabolic equation on the density ρ and the vorticity curl v , and as a transport equation on the divergence div v . We show the existence of strong solution with large initial data in finite time when ( ρ 0 − 1) ∈ B N p p, 1 . A remarkable feature of this solution is the regularizing effects on the density. We extend this result to the case of global strong solution with small initial data.
Subjects / KeywordsNavier-Stokes equations
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