In this study, we analyze the Landau equation with soft potentials under spatially homogeneous conditions. Our primary objective is to establish the existence, uniqueness, and global dynamics of the solution when a perturbation is introduced to the initially non-negative background solution. Notably, this perturbation is allowed to have negative values. Additionally, we explore the practical application of spectral methods in achieving local-in-time stability for solving the Landau equation.

何凌冰, 2007年博士毕业于中科院数学与系统科学研究院, 后加入清华大学数学科学系。现任清华大学数学科学系教授、博士生导师, 主要研究领域为动理学方程与流体力学方程组。在JEMS, Annales de l'ENS, CMP, ARMA等数学杂志发表论文30余篇。