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

DOI10.1016/j.matpur.2018.06.025zbMath1417.37235arXiv1803.02641OpenAlexW2964076002WikidataQ129602234 ScholiaQ129602234MaRDI QIDQ2317072

Denis Serre

Publication date: 8 August 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.02641

zbMATH Keywords

integrabilityMaxwell's equationsdeterminantVlasov-Poisson equationdivergence-free tensors

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Foundations in optics and electromagnetic theory (78A02) Vlasov equations (35Q83) Maxwell equations (35Q61) Monge-Ampère equations (35J96)

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Mixed determinants, compensated integrability, and new a priori estimates in gas dynamics ⋮ Lower semi-continuity for 𝒜-quasiconvex functionals under convex restrictions ⋮ Hard spheres dynamics: weak vs strong collisions ⋮ Divergence-Free Tensors and Cofactors in Geometry and Fluid Dynamics ⋮ Galilean theory of dispersion for kinetic equations ⋮ Source-solutions for the multi-dimensional Burgers equation ⋮ Divergence and determinant of positive symmetric tensors ⋮ Projective properties of divergence-free symmetric tensors, and new dispersive estimates in gas dynamics ⋮ Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates ⋮ On the upper semicontinuity of a quasiconcave functional

Cites Work

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