Mixed determinants, Compensated Integrability and new {\em a priori} estimates in Gas dynamics
Résumé
We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over ${\bf Sym}_n(\R)$. This allows us to establish new {\em a priori} estimates for inviscid gases flowing in the whole space ${\mathbb R}^d$. Notably, we estimate the defect measure (Boltzman equation) or weighted spacial correlations of the velocity field (Euler system). As usual, our bounds involve only the total mass and energy of the flow.
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