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
16 Citations
• 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
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
• D. Serre
• 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
• 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
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
• 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 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 • 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 • Mathematics Journal of Functional Analysis • 2020 • Mathematics ESAIM: 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 References SHOWING 1-10 OF 15 REFERENCES We study the existence and uniqueness of solutions of Monge-Ampere-type equations. This type of equations has been studied extensively by Caffarelli, Nirenberg, Spruck and many others. (See [5] • Mathematics • 2005 We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the "primary" • D. Serre • Mathematics Annales de l'Institut Henri Poincaré C, Analyse non linéaire • 2018 Introduction The Kantorovich duality Geometry of optimal transportation Brenier's polar factorization theorem The Monge-Ampere equation Displacement interpolation and displacement convexity Geometric • Mathematics • 1989 We prove that various nonlinear quantities occurring in the compensated compactness theory belong to the Hardy space H 1 . We also indicate some applications, variants and extensions of such results • Mathematics • 2018 AbstractLet Ω be a bounded and connected open subset of ℝN with a Lipschitz-continuous boundary, the set Ω being locally on the same side of ∂Ω. A vector version of a fundamental lemma of J. L. • Mathematics • 1999 The notion of {\cal A}-quasiconvexity is introduced as a necessary and sufficient condition for (sequential) lower semicontinuity of$$ (u,v) \mapsto \int_{\Omega} f(x,u(x), v(x))\, dx  whenever
• Physics
• 1971
ZusammenfassungDie Autoren betrachten allgemeine Stoffe, für die die Energiedichte, die Entropiedichte, die elektrische Induktion, die magnetische Induktion, die elektrische Stromdichte und der