Potential theory for nonlocal drift-diffusion equations

The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to include drifts of critical order belonging merely to BMO. In pa...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Quoc-Hung, Nguyen, Nowak, Simon, Sire, Yannick, Weidner, Marvin
Format: Article
Language:English
Subjects:
Divergence
Drift
Estimates
Mathematical analysis
Potential theory
Online Access:Get full text
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Summary:The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to include drifts of critical order belonging merely to BMO. In particular, our results allow to derive new estimates for the dissipative surface quasi-geostrophic equation.
ISSN:2331-8422