Weak-Strong Uniqueness for the Landau Equation by a Relative Entropy Method
Abstract
Abstract. We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in stability estimates. The logarithmic derivatives of the strong solution are required to have polynomial growth, while the weak solution can be any H-solution with sufficiently many moments at initial time. Since we require a substantial amount of regularity on the strong solution, we also provide an example of sufficient conditions on the initial data that ensure this regularity in the Coulomb (and very soft potentials) case.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Numerical methods in inverse problems
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 5
- Pages
- 4601–4640
- Publication date
- 9 September 2026
- Language
- EN