Mathematical Research Letters

Volume 29 (2022)

Number 4

Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

Pages: 945 – 960



Jann-Long Chern (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Maria Gualdani (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)


We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in the space $L^\infty (0, T, L^p (\mathbb{R}^3))$ for some $p \gt 3/2$. The proof uses a weighted Poincaré–Sobolev inequality recently introduced in [11].

JLC is supported by NSTC 110-2115-M-003-019-MY3 and NSTC 111-2218-E-008-004-MBK. MPG is supported by NSF DMS-2019335.

JLC and MPG would like to thank KTH Royal Institute of Technology and then NCTS Mathematics Division Taipei for their kind hospitality.

Received 23 March 2020

Accepted 21 July 2020

Published 23 February 2023