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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Contributor : Denis Serre <>
Submitted on : Monday, November 13, 2017 - 2:25:14 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
Long-term archiving on : Wednesday, February 14, 2018 - 2:42:43 PM

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  • HAL Id : ensl-01514880, version 4
  • ARXIV : 1705.00331

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Denis Serre. Divergence-free positive symmetric tensors and fluid dynamics. 2017. ⟨ensl-01514880v4⟩

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