Local well-posedness for a class of singular Vlasov equations

DOI10.3934/krm.2022027zbMath1524.35647arXiv2202.07287OpenAlexW4291137201MaRDI QIDQ6106895

Thomas Chaub

Publication date: 3 July 2023

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.07287

zbMATH Keywords

local well-posednessSobolev regularityquasineutral limitVlasov equationsaveraging lemmas

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Vlasov equations (35Q83) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Regularity of the moments of the solution of a transport equation
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• On classical solutions in the large in time of two-dimensional Vlasov's equation
• On Vlasov-Manev equations. II: Local existence and uniqueness
• On Vlasov-Manev equations. I: Foundations, properties, and nonglobal existence
• The ``Jeans swindle: a true story -- mathematically speaking.
• Elliptic partial differential equations of second order
• The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits
• Ill-posedness of the hydrostatic Euler and singular Vlasov equations
• Quasineutral limit for Vlasov-Poisson with Penrose stable data
• Global existence of smooth solutions to the vlasov poisson system in three dimensions
• Stable Ground States and Self-Similar Blow-Up Solutions for the Gravitational Vlasov--Manev System

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