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

Yasunori Maekawa, Hideyuki Miura

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)123-191
ページ数69
ジャーナルAdvances in Mathematics
247
DOI
出版ステータスPublished - 2013 11

ASJC Scopus subject areas

  • 数学 (全般)

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