### 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) |
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Pages (from-to) | 255-266 |

Number of pages | 12 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2012 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Mathematical Fluid Mechanics*,

*14*(2), 255-266. https://doi.org/10.1007/s00021-011-0054-1

**Higher regularity of hölder continuous solutions of parabolic equations with singular drift velocities.** / Friedlander, Susan; Vicol, Vlad.

Research output: Contribution to journal › Article

*Journal of Mathematical Fluid Mechanics*, vol. 14, no. 2, pp. 255-266. https://doi.org/10.1007/s00021-011-0054-1

}

TY - JOUR

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

AU - Friedlander, Susan

AU - Vicol, Vlad

PY - 2012/6/1

Y1 - 2012/6/1

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

UR - http://www.scopus.com/inward/record.url?scp=84863695073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863695073&partnerID=8YFLogxK

U2 - 10.1007/s00021-011-0054-1

DO - 10.1007/s00021-011-0054-1

M3 - Article

VL - 14

SP - 255

EP - 266

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 2

ER -