LOW-REGULARITY SOLUTIONS TO FOKKER-PLANCK-TYPE SYSTEMS IN THE WHOLE SPACE  

作　　者：Lihua TAN Yingzhe FAN 谈丽华;樊迎哲(School of Mathematics and Statistics,Hubei University of Education,Wuhan 430205,China;School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China)

机构地区：[1]School of Mathematics and Statistics,Hubei University of Education,Wuhan 430205,China [2]School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China

出　　处：《Acta Mathematica Scientia》2024年第6期2361-2390,共30页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(11801285,12326337)。

摘　　要：In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).

关 键 词：global existence algebraic time decay rates exponential time decay rates the whole space low regularity space 

分 类 号：O175[理学—数学]