Flows for non-smooth vector fields with subexponentially integrable divergence

Albert Clop; Renjin Jiang; Joan Orobitg; Juan Eugenio Mateu Bennassar

doi:10.1016/j.jde.2016.03.037

Flows for non-smooth vector fields with subexponentially integrable divergence

Albert Clop, Renjin Jiang, Joan Orobitg, Juan Eugenio Mateu Bennassar

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [17]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.

Original language	English
Pages (from-to)	1237-1263
Journal	Journal of Differential Equations
Volume	261
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2016.03.037
Publication status	Published - 15 Jul 2016

Keywords

Divergence
Non-smooth flow
Sobolev vector fields
Transport equation

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10.1016/j.jde.2016.03.037

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title = "Flows for non-smooth vector fields with subexponentially integrable divergence",

abstract = "{\textcopyright} 2016 Elsevier Inc. In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [17]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.",

keywords = "Divergence, Non-smooth flow, Sobolev vector fields, Transport equation",

author = "Albert Clop and Renjin Jiang and Joan Orobitg and {Mateu Bennassar}, {Juan Eugenio}",

year = "2016",

month = jul,

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doi = "10.1016/j.jde.2016.03.037",

language = "English",

volume = "261",

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journal = "Journal of Differential Equations",

issn = "0022-0396",

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TY - JOUR

T1 - Flows for non-smooth vector fields with subexponentially integrable divergence

AU - Clop, Albert

AU - Jiang, Renjin

AU - Orobitg, Joan

AU - Mateu Bennassar, Juan Eugenio

PY - 2016/7/15

Y1 - 2016/7/15

N2 - © 2016 Elsevier Inc. In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [17]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.

AB - © 2016 Elsevier Inc. In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lions [17]. A key ingredient is to use a quantitative estimate of solutions to the Cauchy problem of transport equation to obtain the regularity of density functions.

KW - Divergence

KW - Non-smooth flow

KW - Sobolev vector fields

KW - Transport equation

U2 - 10.1016/j.jde.2016.03.037

DO - 10.1016/j.jde.2016.03.037

M3 - Article

SN - 0022-0396

VL - 261

SP - 1237

EP - 1263

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Flows for non-smooth vector fields with subexponentially integrable divergence

Abstract

Keywords

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