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

Abstract

AbstractIn 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 $$d \geqq 3$$ d ≧ 3 . The physical case of Coulomb interaction in dimension $$d=3$$ 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.