期刊
ADVANCES IN MATHEMATICS
卷 247, 期 -, 页码 123-191出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2013.07.011
关键词
Non-local parabolic equations; Divergence free drift; Fundamental solutions; Nash iteration; 2D dissipative quasi-geostrophic equations
类别
资金
- Japan Society of the Promotion of Science (JSPS) [22740090, 25800079, 21740092, 25707005]
- Grants-in-Aid for Scientific Research [22740090, 25800079, 25707005, 21740092] Funding Source: KAKEN
We are concerned with non-local parabolic 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 continuity estimates, under weak regularity assumptions on the kernel of the non-local term and the velocity of the drift term. As an application, we give an alternative proof of global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case. (C) 2013 Elsevier Inc. All rights reserved.
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