Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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


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 | References | Similar Articles | Additional Information

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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Additional Information

Robert M. Strain
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
MR Author ID: 746810
ORCID: 0000-0002-1107-8570
Email: strain@math.upenn.edu

Zhenfu Wang
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
MR Author ID: 1183905
Email: zwang423@math.upenn.edu

Keywords: Relativistic Landau equation, weak solutions, stochastic representation, uniqueness, Wasserstein distance.
Received by editor(s): March 12, 2019
Received by editor(s) in revised form: May 27, 2019
Published electronically: July 8, 2019
Additional Notes: The first author was partially supported by the NSF grants DMS-1500916 and DMS-1764177.
Dedicated: Dedicated to Professor Walter Strauss on the occasion of his eightieth birthday
Article copyright: © Copyright 2019 Brown University