Sobolev regular flows of non-Lipschitz vector fields

Albert Clop; Heikki Jylhä

doi:10.1016/j.jde.2018.10.002

Sobolev regular flows of non-Lipschitz vector fields

Albert Clop, Heikki Jylhä

Department of Mathematics

Research output: Contribution to journal › Article › Research

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 language	English
Pages (from-to)	4544-4567
Journal	Journal of Differential Equations
Volume	266
DOIs	https://doi.org/10.1016/j.jde.2018.10.002
Publication status	Published - 5 Apr 2019

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title = "Sobolev regular flows of non-Lipschitz vector fields",

abstract = "{\textcopyright} 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.",

author = "Albert Clop and Heikki Jylh{\"a}",

year = "2019",

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doi = "10.1016/j.jde.2018.10.002",

language = "English",

volume = "266",

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T1 - Sobolev regular flows of non-Lipschitz vector fields

AU - Clop, Albert

AU - Jylhä, Heikki

PY - 2019/4/5

Y1 - 2019/4/5

N2 - © 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.

AB - © 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.

U2 - 10.1016/j.jde.2018.10.002

DO - 10.1016/j.jde.2018.10.002

M3 - Article

VL - 266

SP - 4544

EP - 4567

ER -