文献类型：期刊文献

英文题名：SOME A PRIORI ESTIMATES FOR THE HOMOGENEOUS LANDAU EQUATION WITH SOFT POTENTIALS

作者：Alexandre, Radjesvarane[1,2];Liao, Jie[3];Lin, Chunjin[4]

机构：[1]Arts & Metiers Paris Tech, F-75013 Paris, France;[2]Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China;[3]E China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China;[4]Hohai Univ, Coll Sci, Dept Math, Nanjing 210098, Jiangsu, Peoples R China

年份：2015

卷号：8

期号：4

起止页码：617

外文期刊名：KINETIC AND RELATED MODELS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000365079700001)】；

基金：This work is partially supported by Fundamental Research Funds for the Central Universities, National Natural Science Foundation of China (Nos.11171211, 11201116, 11301182), Science and Technology commission of Shanghai Municipality (No. 13ZR1453400), together with a starting grant from Shanghai Jiao Tong University.

语种：英文

外文关键词：Landau equation with soft potentials; weak solutions; entropy dissipation; weighted Fisher information; moment estimates

摘要：This paper is devoted to some a priori estimates for the homogeneous Landau equation with soft potentials. Using coercivity properties of the Landau operator for soft potentials, we prove that the global in time a priori estimates of weak solutions in L-2 space hold true for moderately soft potential cases gamma is an element of [-2,0) without any smallness assumption on the initial data. For very soft potential cases gamma is an element of [-3, 2), which cover in particular the Coulomb case gamma = -3, we get local in time estimates of weak solutions in L-2. In the proofs of these estimates, global ones for the special case gamma = -2 and local ones for very soft potential cases gamma is an element of [-3, -2), the control on time integral of some weighted Fisher information is required, which is an additional a priori estimate given by the entropy dissipation inequality.