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On fundamental solutions for non-local diffusion equations with divergence free drift
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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