Geodesic
Divergence-free positive symmetric tensors and fluid dynamics
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1209-1234

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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)1d−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 ρ1np, where ρ is the mass density, p the pressure and n the space dimension. For kinetic models, the corresponding quantity generalizes Bony's functional.

DOI : 10.1016/j.anihpc.2017.11.002
Keywords: Conservation laws, Gas dynamics, Functional inequalities 
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     title = {Divergence-free positive symmetric tensors and fluid dynamics},
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     pages = {1209--1234},
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Serre, Denis. Divergence-free positive symmetric tensors and fluid dynamics. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1209-1234. doi: 10.1016/j.anihpc.2017.11.002

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