A new monotonicity formula for the spatially homogeneous Landau equation with Coulomb potential and its applications

IF 2.5 1区数学 Q1 MATHEMATICS

Journal of the European Mathematical Society Pub Date : 2020-10-31 DOI:10.4171/jems/1313

L. Desvillettes, Lingbing He, Jin-Cheng Jiang

引用次数: 13

Abstract

We describe a time-dependent functional involving the relative entropy and the $\dot{H}^1$ seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functionial sheds light on the competition between the dissipation and the nonlinearity for this equation. It enables to obtain new results concerning regularity/blowup issues for the Landau equation with Coulomb potential.

查看原文本刊更多论文

具有库仑势的空间齐次朗道方程的一个新的单调性公式及其应用

我们描述了一个涉及相对熵和$\dot{H}^1$半模的时变泛函，它沿具有库仑势的空间齐次朗道方程的解减小。该单调泛函的研究揭示了该方程的耗散与非线性之间的竞争。它可以得到关于具有库仑势的朗道方程的正则性/爆破问题的新结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the European Mathematical Society 数学-数学

CiteScore

4.50

自引率

0.00%

发文量

103

审稿时长

6-12 weeks

期刊介绍： The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.