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期刊论文

On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion

Changxing MiaoLiutang Xue

SIAM J. Math. Anal.,2019,51(4): 2927-2970 | 2019年02月15日 | 10.1137/17M1158537

URL:https://doi.org/10.1137/17M1158537

摘要/描述

In this paper we address the regularity issues of drift-diffusion equation with nonlocal diffusion, where the diffusion operator is in the realm of stable-type L\'evy operator and the velocity field is defined from the considered quantity by a zero-order pseudo-differential operator. Through using the method of nonlocal maximum principle in a unified way, we prove the eventual regularity result in the supercritical type cases and the global regularity at some logarithmically supercritical cases. The feature of these results is that the time after which the solution is smoothly regular in the supercritical type cases can be evaluated explicitly.

版权说明:以下全部内容由苗长兴上传于   2019年11月13日 18时41分05秒,版权归本人所有。

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