On a wave kinetic equation with resonance broadening in oceanography and atmospheric sciences

TL;DR

This paper introduces a modified three-wave kinetic equation with resonance broadening tailored for oceanography, establishing global existence and uniqueness of strong solutions, advancing the mathematical modeling of stratified ocean flows.

Contribution

It presents a new formulation of resonance broadening in wave kinetic equations, specifically designed for ocean applications, and proves the global well-posedness of the model.

Findings

Established global existence of solutions

Proved uniqueness of strong solutions

Enhanced model suitability for oceanographic phenomena

Abstract

In this work, we study a three-wave kinetic equation with resonance broadening arising from the theory of stratified ocean flows. Unlike Gamba-Smith-Tran(On the wave turbulence theory for stratified flows in the ocean, Math. Models Methods Appl. Sci. 30 (2020), no.1, 105--137), we employ a different formulation of the resonance broadening, which makes the present model more suitable for ocean applications. We establish the global existence and uniqueness of strong solutions to the new resonance broadening kinetic equation.