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Jang, Jinwoo
기하학 수리물리 연구단
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Compactness properties and local existence of weak solutions to the landau equation

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Title
Compactness properties and local existence of weak solutions to the landau equation
Author(s)
Hyung Ju Hwang; Jin Woo Jang
Subject
Boltzmann equation, ; Collisional kinetic theory, ; Landau equation, ; Velocity averages
Publication Date
2020-09
Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.148, no.12, pp.5141 - 5157
Publisher
AMER MATHEMATICAL SOC
Abstract
© 2020 American Mathematical Society. We consider the Landau equation nearby the Maxwellian equilibrium. Based on the assumptions on the boundedness of mass, energy, and entropy in the sense of Silvestre [J. Diffential Equations 262 (2017), no. 3, 3034–3055], we enjoy the locally uniform ellipticity of the linearized Landau operator to derive local-in-time L∞x,v uniform bounds. Then we establish a compactness theorem for the sequence of solutions using the L∞x,v bounds and the standard velocity averaging lemma. Finally, we pass to the limit and prove the local existence of a weak solution to the Cauchy problem. The highlight of this work is in the low-regularity setting where we only assume that the initial condition f0 is bounded in L∞x,v, whose size determines the maximal time-interval of the existence of the weak solution
URI
https://pr.ibs.re.kr/handle/8788114/7624
DOI
10.1090/proc/15173
ISSN
0002-9939
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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