Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities

Susan Friedlander; Vlad Vicol

doi:10.1007/s00021-011-0054-1

Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities

Susan Friedlander, Vlad Vicol

Mathematics

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

9 Scopus citations

Abstract

Motivated by an equation arising in magnetohydrodynamics, we prove that Hölder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the Hölder exponent of the weak solutions.

Original language	English (US)
Pages (from-to)	255-266
Number of pages	12
Journal	Journal of Mathematical Fluid Mechanics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/s00021-011-0054-1
State	Published - Jun 2012

All Science Journal Classification (ASJC) codes

Mathematical Physics
Condensed Matter Physics
Computational Mathematics
Applied Mathematics

Keywords

Higher regularity
Magneto-geostrophic model
Space-time Besov spaces
Weak solutions

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10.1007/s00021-011-0054-1

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title = "Higher regularity of h{\"o}lder continuous solutions of parabolic equations with singular drift velocities",

abstract = "Motivated by an equation arising in magnetohydrodynamics, we prove that H{\"o}lder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the H{\"o}lder exponent of the weak solutions.",

keywords = "Higher regularity, Magneto-geostrophic model, Space-time Besov spaces, Weak solutions",

author = "Susan Friedlander and Vlad Vicol",

note = "Funding Information: Acknowledgements. The work of S.F. was in part supported by the NSF grant DMS 0803268. The authors would like to thank Peter Constantin for fruitful discussions on the topic, and for pointing out the advantage of space–time Besov spaces.",

year = "2012",

month = jun,

doi = "10.1007/s00021-011-0054-1",

language = "English (US)",

volume = "14",

pages = "255--266",

journal = "Journal of Mathematical Fluid Mechanics",

issn = "1422-6928",

publisher = "Birkhauser Verlag Basel",

number = "2",

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T1 - Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities

AU - Friedlander, Susan

AU - Vicol, Vlad

N1 - Funding Information: Acknowledgements. The work of S.F. was in part supported by the NSF grant DMS 0803268. The authors would like to thank Peter Constantin for fruitful discussions on the topic, and for pointing out the advantage of space–time Besov spaces.

PY - 2012/6

Y1 - 2012/6

N2 - Motivated by an equation arising in magnetohydrodynamics, we prove that Hölder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the Hölder exponent of the weak solutions.

AB - Motivated by an equation arising in magnetohydrodynamics, we prove that Hölder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner (J Differ Equ 121(2):314-328, 1995), combined with energy estimates, without any minimality assumption on the Hölder exponent of the weak solutions.

KW - Higher regularity

KW - Magneto-geostrophic model

KW - Space-time Besov spaces

KW - Weak solutions

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VL - 14

SP - 255

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JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 2

ER -

Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities

Abstract

All Science Journal Classification (ASJC) codes

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