Lagrangian flows for vector fields with anisotropic regularity

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Lagrangian flows for vector fields with anisotropic regularity

JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)

ID	3343803
Author(s)	Bohun, Anna; Bouchut, Francois; Crippa, Gianluca
Author(s) at UniBasel	Crippa, Gianluca
Year	2016
Year: comment	In press
Title	Lagrangian flows for vector fields with anisotropic regularity
Journal	Annales de l'Institut Henri Poincaré (C) Analyse non linéaire
Volume	33
Number	6
Pages / Article-Number	1409-1429
Abstract	We prove quantitative estimates for flows of vector fields subject to anisotropic regularity conditions: some derivatives of some components are (singular integrals of) measures, while the remaining derivatives are (singular integrals of) integrable functions. This is motivated by the regularity of the vector field in the Vlasov-Poisson equation with measure density. The proof exploits an anisotropic variant of the argument in [Crippa-De Lellis, Bouchut-Crippa] and suitable estimates for the difference quotients in such anisotropic context. In contrast to regularization methods, this approach gives quantitative estimates in terms of the given regularity bounds. From such estimates it is possible to recover the well posedness for the ordinary differential equation and for Lagrangian solutions to the continuity and transport equations.
Publisher	Elsevier
ISSN/ISBN	0294-1449
edoc-URL	http://edoc.unibas.ch/40176/
Full Text on edoc	Restricted
Digital Object Identifier DOI	10.1016/j.anihpc.2015.05.005
ISI-Number	CCC:000389108400001
Document type (ISI)	Article

15/05/2024

Research Database / FORSCHUNGSDATENBANK