Divergence-free positive symmetric tensors and fluid dynamics
نویسنده
چکیده
We consider d× d tensors A(x) that are symmetric, positive semi-definite, and whose rowdivergence vanishes identically. We establish sharp inequalities for the integral of (detA) 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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