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Title: Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition

We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the \begin{document}$ S_p $\end{document} estimate of [7], we prove regularity in the kinetic Sobolev spaces \begin{document}$ S_p $\end{document} and anisotropic Hölder spaces for such weak solutions. Such \begin{document}$ S_p $\end{document} regularity leads to the uniqueness of weak solutions.

Authors:
; ;
Award ID(s):
2055244
Publication Date:
NSF-PAR ID:
10321247
Journal Name:
Kinetic and Related Models
Volume:
15
Issue:
3
ISSN:
1937-5093
Sponsoring Org:
National Science Foundation
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