Global Existence for an Isotropic Landau Model

2024/03/16 by Bowman, David, Ji, Sehyun
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.10810

Abstract

Following the recent ideas of Guillen and Silvestre in [9], we prove that the Fisher information is non-increasing along the flow of the isotropic Landau equation. We then use this fact to deduce global existence for the equation ∂_t f = (-Δ)^-1f ⋅ Δf + f² under a relatively lax set of conditions on the initial data. In particular, we remove the restrictive radially decreasing assumption of previous works.

Related

• Dissipation estimates of the Fisher information for the Landau equation
• Production of the Fisher information for the Landau-Coulomb equation with L1 initial data
• Global existence for an isotropic modification of the Boltzmann equation
• The Landau equation does not blow up
• Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials