# Compensated integrability. Applications to the Vlasov–Poisson equation and other models in mathematical physics

@article{Serre2018CompensatedIA, title={Compensated integrability. Applications to the Vlasov–Poisson equation and other models in mathematical physics}, author={Denis Serre}, journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es}, year={2018} }

## 16 Citations

### Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics

- MathematicsQuarterly of Applied Mathematics
- 2022

We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over
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### Multi-dimensional scalar conservation laws with unbounded integrable initial data

- Mathematics
- 2018

We discuss the minimal integrability needed for the initial data, in order that the Cauchy problem for a multi-dimensional conservation law admit an entropy solution. In particular we allow unbounded…

### Symmetric Divergence-free tensors in the Calculus of Variations

- MathematicsComptes Rendus. Mathématique
- 2022

Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called “second” variational principle, where the…

### Compensation phenomena for concentration effects via nonlinear elliptic estimates

- Mathematics
- 2021

. We study compensation phenomena for ﬁelds satisfying both a pointwise and a linear diﬀerential constraint. This eﬀect takes the form of nonlinear elliptic estimates, where constraining the values…

### Estimating the number and the strength of collisions in molecular dynamics

- Physics
- 2019

We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of…

### Source-Solutions for the Multi-dimensional Burgers Equation

- MathematicsArchive for Rational Mechanics and Analysis
- 2020

We have shown in a recent collaboration that the Cauchy problem for the multi-dimensional Burgers equation is well-posed when the initial data u (0) is taken in the Lebesgue space $$L^1({{\mathbb…

### Hard spheres dynamics: weak vs hard collisions

- Mathematics, Physics
- 2020

We consider the motion of a finite though large number $N$ of hard spheres in the whole space $\mathbb{R}^n$. Particles move freely until they experience elastic collisions. We use our recent theory…

### Projective Properties of Divergence-Free Symmetric Tensors, and New Dispersive Estimates in Gas Dynamics

- MathematicsMilan Journal of Mathematics
- 2021

The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves…

### On the upper semicontinuity of a quasiconcave functional

- MathematicsJournal of Functional Analysis
- 2020

### Lower semi-continuity for $\mathcal A$-quasiconvex functionals under convex restrictions

- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2021

We show weak lower semi-continuity of functionals assuming the new notion of a ``convexly constrained'' $\mathcal A$-quasiconvex integrand. We assume $\mathcal A$-quasiconvexity only for functions…

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