A Priori Estimates for Solutions to Landau Equation Under Prodi–Serrin Like Criteria

Abstract

In this paper, we introduce Prodi–Serrin like criteria which enable us to provide a priori estimates for the solutions to the spatially homogeneous Landau equation for all classical soft potentials and dimensions \(d \geqq 3\). The physical case of Coulomb interaction in dimension \(d=3\) is included in our analysis; this generalizes the work of Silvestre (J Differ Equ 262:3034–3055, 2017). Our approach is quantitative and does not require a preliminary knowledge of elaborate tools for nonlinear parabolic equations.