Sobolev regular flows of non-Lipschitz vector fields

Albert Clop, Heikki Jylhä

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)

Abstract

© 2018 Elsevier Inc. We show that vector fields with exponentially integrable derivatives admit a well defined flow of homeomorphisms X(t,⋅)∈W1,p(t)loc for some p(t)>1, at least for small times. When the field is certain Riesz potential of a bounded function, the result becomes global in time, due to techniques from Geometric Function Theory. The local result also applies to the flows arising from Yudovich solutions to the planar Euler system with bounded vorticity.
Original languageEnglish
Pages (from-to)4544-4567
JournalJournal of Differential Equations
Volume266
DOIs
Publication statusPublished - 5 Apr 2019

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