Uniqueness of bounded solutions for the homogeneous relativistic Landau equation with Coulomb interactions

Strain, Robert; Wang, Zhenfu

doi:10.1090/qam/1545

Authors: Robert M. Strain and Zhenfu Wang
Journal: Quart. Appl. Math. 78 (2020), 107-145
MSC (2010): Primary 82D10, 35Q70, 35Q75, 35B45, 35A02.
DOI: https://doi.org/10.1090/qam/1545
Published electronically: July 8, 2019
MathSciNet review: 4042221
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Abstract: We prove the uniqueness of weak solutions to the spatially homogeneous special relativistic Landau equation under the conditional assumption that the solution satisfies $(p^0)^7 F(t,p) \in L^1 ([0,T]; L^\infty )$. The existence of standard weak solutions to the relativistic Landau equation has been shown recently in [J. Funct. Anal. 277 (2019), pp. 1139–1201].

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