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## Mixed determinants, Compensated Integrability and new {\em a priori} estimates in Gas dynamics

Denis Serre
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#### Abstract

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.

### Dates and versions

ensl-03945122 , version 1 (10-02-2023)

### Identifiers

• HAL Id : ensl-03945122 , version 1
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### Cite

Denis Serre. Mixed determinants, Compensated Integrability and new {\em a priori} estimates in Gas dynamics. 2022. ⟨ensl-03945122⟩

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