On fundamental solutions for non-local parabolic equations with divergence free drift
On fundamental solutions for non-local parabolic equations with divergence free drift
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DOI：
10.1016/j.aim.2013.07.011
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发表时间：
2013-11
影响因子：
1.7
通讯作者：
Yasunori Maekawa;H. Miura
中科院分区：
文献类型：
--
作者：
Yasunori Maekawa;H. Miura
本文研究了具有散度自由漂移项的非局部抛物型方程。通过使用经典的Nash方法，我们证明了基本解的存在性与连续性估计，在弱正则性假设下的非局部项的核和漂移项的速度。作为应用，我们给出了临界情形下二维耗散准地转方程整体正则性的另一种证明。
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.