Communications in Mathematical Sciences
Volume 16 (2018)
Smoothing effects and decay estimate of the solution of the linearized two-species Landau equation
Pages: 2261 – 2300
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.
Landau equation, large-time behavior, smoothing effects
2010 Mathematics Subject Classification
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