Local and global existence of a nonlocal equation with a singular integral drift term

Journal of Nonlinear Sciences and Applications Pub Date : 2021-03-19 DOI:10.22436/jnsa.015.01.05

Ying-Ling Lu

引用次数: 0

Abstract

We study an initial value problem with fractional Laplacian and a singular integral drift term. This equation quantifies fractal interfaces in statistical mechanics. The singularity of the drift term is a generalization of existing results. Making use of some important boundedness properties of Calderón-Zygmund operator in Lp and Lipschitz spaces, we obtain local and global existence theorems.

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具有奇异积分漂移项的非局部方程的局部和全局存在性

研究了一类具有分数阶拉普拉斯算子和奇异积分漂移项的初值问题。这个方程量化了统计力学中的分形界面。漂移项的奇异性是对已有结果的推广。利用Calderón-Zygmund算子在Lp和Lipschitz空间中的一些重要有界性，得到了局部存在性定理和全局存在性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.