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}
}
  • D. Serre
  • Published 5 March 2018
  • Mathematics
  • Journal de Mathématiques Pures et Appliquées
View PDF on arXiv
16 Citations
Background Citations
1
Methods Citations
2

16 Citations

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

  • D. Serre
  • Mathematics
    Quarterly of Applied Mathematics
  • 2022
We extend the scope of our recent Compensated Integrability theory, by exploiting the multi-linearity of the determinant map over S y m n ( R ) \mathbf {Sym}_n(\mathbb…

Multi-dimensional scalar conservation laws with unbounded integrable initial data

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

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  • Mathematics
    Comptes 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

. 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

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

  • D. Serre
  • Mathematics
    Archive 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

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

  • D. Serre
  • Mathematics
    Milan 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

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

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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  • Mathematics
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