Local existence of strong solutions to the capillary wave kinetic equation

Abstract

In this paper, we follow Pan-Wu's idea [PW26] to prove local existence of the capillary wave kinetic equation. To be more specific, we will linearize the nonlinear operator and decompose it into dissipative part and bounded part. The main difficulty comes from the fact that the collision kernel has less symmetry compared with the one in gravity water wave. To overcome it, we are required to choose and pair each term delicately.