2024-03-29T05:30:49Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698192022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116On fundamental solutions for non-local diffusion equations with divergence free driftMaekawa, YasunoriHideyuki, Miuraopen accessnon-local diffusion equationsdivergence free driftfundamental solutionsNash iteration2D dissipative quasi-geostrophic equations.410We 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.Department of Mathematics, Hokkaido University2012-07-17engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84160http://hdl.handle.net/2115/6981910.14943/84160Hokkaido University Preprint Series in Mathematics1014146https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69819/1/pre1014.pdfapplication/pdf331.02 KB2012-07-17