ON THE INITIAL-VALUE PROBLEM FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM WITH INITIAL DATA IN L(P) SPACES

被引:63
作者
CARRILLO, JA
SOLER, J
机构
[1] Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Granada
关键词
D O I
10.1002/mma.1670181006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper the global existence of weak solutions for the Vlasov-Poisson-Fokker-Planck equations in three dimensions is proved with an L(1) boolean AND L(p) initial data. Also, the global existence of weak solutions in four dimensions with small initial data is studied. A convergence of the solutions is obtained to those built by E. Horst and R. Hunze when the Fokker-Planck term vanishes. In order to obtain the a priori necessary estimates a sequence of approximate problems is introduced. This sequence is obtained starting from a non-linear regularization of the problem together with a linearization via a time retarded mollification of the non-linear term. The a priori bounds are reached by means of the control of the kinetic energy in the approximate sequence of problems. Then, the proof is completed obtaining the equicontinuity properties which allow to pass to the limit.
引用
收藏
页码:825 / 839
页数:15
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