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On propagation of
higher space regularity for nonlinear Vlasov equations
Daniel Han-Kwan |
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Vol. 12 (2019), No. 1, 189–244
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Abstract |
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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. |
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Keywords
kinetic transport equations, kinetic averaging lemmas
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Mathematical Subject Classification 2010
Primary: 35Q83
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Milestones
Received: 12 October 2017
Revised: 19 March 2018
Accepted: 19 April 2018
Published: 2 August 2018
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Authors |
| Daniel Han-Kwan | |
| CMLS École polytechnique CNRS Palaiseau France |
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