On the monotonicity of the entropy production in the Landau-Maxwell equation
Abstract
We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing when the directional temperatures are well-distributed. It implies that for any initial condition with finite mass and energy, the entropy production is guaranteed to be non-increasing after a certain explicit time. We also obtain exponential decay of the entropy production. We provide an explicit formula for the derivative of the entropy production which may be a starting point for future progress towards full monotonicity.
Fields of Study & Subjects
Advanced Thermodynamics and Statistical Mechanics
Gas Dynamics and Kinetic Theory
Navier-Stokes equation solutions
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 January 2026
- Language
- EN
- Document type
- Preprint