Asymptotics Toward Viscous Contact Waves for Solutions of the Landau Equation
Asymptotics Toward Viscous Contact Waves for Solutions of the Landau Equation
复制标题
兰道方程解的粘性接触波渐进性
DOI：
10.1007/s00220-022-04405-x
复制
发表时间：
2021-03
影响因子：
2.4
通讯作者：
喻洪俊
中科院分区：
文献类型：
--
作者：
Duan Renjun;Yang Dongcheng;喻洪俊
在本文中，我们关注的是，涉及粘性接触波的巨大时间渐近，以实现物理逼真的库仑相互作用，以解决Landau方程的解决方案。确切地说，对于在空间上的二维中相应的库奇问题
In the paper, we are concerned with the large time asymptotics toward the viscous contact waves for solutions of the Landau equation with physically realistic Coulomb interactions. Precisely, for the corresponding Cauchy problem in the spatially one-dimensional setting, we construct the unique global-in-time solution near a local Maxwellian whose fluid quantities are the viscous contact waves in the sense of hydrodynamics and also prove that the solution tends toward such local Maxwellian in large time. The result is proved by elaborate energy estimates and seems the first one on the dynamical stability of contact waves for the Landau equation. One key point of the proof is to introduce a new time-velocity weight function that includes an exponential factor of the formwith \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} q(t):=q_1-q_2\int _0^tq_3(s)\,ds, \end{aligned}$$\end{document}whereandare given positive constants andis defined by the energy dissipation rate of the solution itself. The time derivative of such weight function is able to induce an extra quartic dissipation term for treating the large-velocity growth in the nonlinear estimates due to degeneration of the linearized Landau operator in the Coulomb case. Note that in our problem the explicit time-decay of solutions around contact waves is unavailable but no longer needed under the crucial use of the above weight function, which is different from the situation in Duan (Ann Inst H Poincaré Anal Non Linéaire 31:751–778, 2014) and Duan and Yu (Adv Math 362:106956, 2020).
登录
查看更多内容
当地麦克斯韦系统附近的弗拉索夫-泊松-朗道系统
影响因子：
1.7
作者：
Duan Renjun;喻洪俊
通讯作者：
喻洪俊
具有接近局部麦克斯韦方程的软势的玻尔兹曼方程
影响因子：
2.5
作者：
Xin, Zhouping;Yang, Tong;Yu, Hongjun
通讯作者：
Yu, Hongjun
影响因子：
64.8
作者：
R. H. Fowler
通讯作者：
R. H. Fowler
影响因子：
3.9
作者：
Yan Guo
通讯作者：
Yan Guo
DOI：
10.1007/s42543-019-00018-x
发表时间：
2020-01
期刊：
--
影响因子：
--
作者：
Jinoh Kim;Yan Guo;H. Hwang
通讯作者：
Jinoh Kim;Yan Guo;H. Hwang