Communications in Mathematical Sciences

Volume 16 (2018)

Number 8

Smoothing effects and decay estimate of the solution of the linearized two-species Landau equation

Pages: 2261 – 2300

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n8.a9

Authors

Yu-Chu Lin (Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan)

Haitao Wang (Institute of Natural Sciences and School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China)

Kung-Chien Wu (Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan; and National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan)

Abstract

We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption on the initial data, it is shown that the solution becomes smooth instantaneously in both the space and momentum variables. Moreover, the large-time behavior of the solution is also obtained.

Keywords

Landau equation, large-time behavior, smoothing effects

2010 Mathematics Subject Classification

35Q20, 82C40

Full Text (PDF format)

The authors want to thank Professor Tai-Ping Liu for helpful comments. Y.-C. Lin was supported by the Ministry of Science and Technology under the grant MOST 107-2115-M-006-006 -. H.T. Wang was sponsored by Shanghai Sailing Program (Grant No. 18YF1411800) and Shanghai Jiao Tong University (Grant No. WF220441907). K.-C. Wu was supported by the Ministry of Science and Technology under the grant MOST 108-2636-M-006-005-MY4 and National Center for Theoretical Sciences.

Received 22 March 2018

Accepted 22 August 2018

Published 18 April 2019