COMPACTNESS PROPERTIES AND LOCAL EXISTENCE OF WEAK SOLUTIONS TO THE LANDAU EQUATION
SCIE
SCOPUS
- Title
- COMPACTNESS PROPERTIES AND LOCAL EXISTENCE OF WEAK SOLUTIONS TO THE LANDAU EQUATION
- Authors
- Hwang, H.J.; Jang, J.W.
- Date Issued
- 2020-12
- Publisher
- AMER MATHEMATICAL SOC
- Abstract
- 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(infinity) uniform bounds. Then we establish a compactness theorem for the sequence of solutions using the L-x,v(infinity) 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 f(0) is bounded in L-x,v(infinity) whose size determines the maximal time-interval of the existence of the weak solution.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/105408
- DOI
- 10.1090/proc/15173
- ISSN
- 0002-9939
- Article Type
- Article
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 148, no. 12, page. 5141 - 5157, 2020-12
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