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Preprints, Working Papers, ... Year : 2017

Divergence-free positive symmetric tensors and fluid dynamics

Abstract

We consider d × d tensors A(x) that are symmetric, positive semi-definite, and whose row-divergence vanishes identically. We establish sharp inequalities for the integral of (det A) 1 d−1. We apply them to models of compressible inviscid fluids: Euler equations, Euler–Fourier, relativistic Euler, Boltzman, BGK, etc... We deduce an a priori estimate for a new quantity, namely the space-time integral of ρ 1 n p, where ρ is the mass density, p the pressure and n the space dimension. For kinetic models, the corresponding quantity generalizes Bony's functional.
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Dates and versions

ensl-01514880 , version 1 (26-04-2017)
ensl-01514880 , version 2 (15-05-2017)
ensl-01514880 , version 3 (29-06-2017)
ensl-01514880 , version 4 (13-11-2017)

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Denis Serre. Divergence-free positive symmetric tensors and fluid dynamics. 2017. ⟨ensl-01514880v1⟩
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