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On fundamental solutions for non-local diffusion equations with divergence free drift

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Title: On fundamental solutions for non-local diffusion equations with divergence free drift
Authors: Maekawa, Yasunori Browse this author
Hideyuki, Miura Browse this author
Keywords: non-local diffusion equations
divergence free drift
fundamental solutions
Nash iteration
2D dissipative quasi-geostrophic equations.
Issue Date: 17-Jul-2012
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1014
Start Page: 1
End Page: 46
Abstract: We are concerned with non-local diffusion equations in the presence of a divergence free drift term. By using the classical Nash approach we show the existence of fundamental solutions, together with the continuity estimates, under weak regularity assumptions on the kernel of the diffusion term and the velocity of the drift term. As an application, our result gives the alternative proof of the global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69819
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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