Linear stability of traveling Maxwellians for Landau equation with very soft potentials

Sanchit Chaturvedi, Jonathan Luk

Abstract

Consider the Landau equation with a Coulomb potential linearized around traveling Maxwellians. We prove that the microscopic part of the linear solution decays with an inverse polynomial rate, while the macroscopic part remains bounded but in general does not decay. In particular, the long-time dynamics are different from the linearization around either (1) traveling Maxwellians for moderately soft or hard potentials or (2) global (non-traveling) Maxwellians (for any potentials).

Disclosure

“the microscopic part of the solution. Acknowledgement. SC acknowledges support by the Simons Foundation Award 1141490. JL gratefully acknowledges the support of a National Science Foundation Grant under DMS-2304445. AI Disclosure. We used Anthropic Claude to proofread earlier versions of the paper. The paper is completely written by the authors and the mathematical content is the authors’ own. 2. Notations We introduce the notations we use in the re”
PDF page 8

Classification: Proofreading, grammar, or spelling
Multiplier: 1
Verified: 2026-08-22T18:33:02.029759Z

Structural counts

Pages 58 pdf

Theorems 5 source

Lemmas 23 source

Propositions 29 source

Corollaries 8 source

Definitions 4 source

Displayed equations 384 source

Bibliography entries 846 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Traveling.Maxwellians.260818.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.