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2019 On propagation of higher space regularity for nonlinear Vlasov equations
Daniel Han-Kwan
Anal. PDE 12(1): 189-244 (2019). DOI: 10.2140/apde.2019.12.189

Abstract

This work is concerned with the broad question of propagation of regularity for smooth solutions to nonlinear Vlasov equations. For a class of equations (that includes Vlasov–Poisson and relativistic Vlasov–Maxwell systems), we prove that higher regularity in space is propagated, locally in time, into higher regularity for the moments in velocity of the solution. This in turn can be translated into some anisotropic Sobolev higher regularity for the solution itself, which can be interpreted as a kind of weak propagation of space regularity. To this end, we adapt the methods introduced by D. Han-Kwan and F. Rousset (Ann. Sci. École Norm. Sup. 49:6 (2016) 1445–1495) in the context of the quasineutral limit of the Vlasov–Poisson system.

Citation

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Daniel Han-Kwan. "On propagation of higher space regularity for nonlinear Vlasov equations." Anal. PDE 12 (1) 189 - 244, 2019. https://doi.org/10.2140/apde.2019.12.189

Information

Received: 12 October 2017; Revised: 19 March 2018; Accepted: 19 April 2018; Published: 2019
First available in Project Euclid: 16 August 2018

zbMATH: 06930186
MathSciNet: MR3842911
Digital Object Identifier: 10.2140/apde.2019.12.189

Subjects:
Primary: 35Q83

Keywords: kinetic averaging lemmas , kinetic transport equations

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2019
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