On the wave turbulence theory for stratified flows in the ocean
Irene M. Gamba, Leslie M. Smith, Minh-Binh Tran
TL;DR
This paper provides the first rigorous mathematical analysis of a wave turbulence equation modeling oceanic internal gravity waves, establishing global existence and uniqueness of solutions.
Contribution
It offers the first rigorous proof of global existence and uniqueness for the wave turbulence equation related to stratified ocean flows.
Findings
Proved global existence of strong solutions
Established uniqueness of solutions
Mathematically validated the wave turbulence model
Abstract
After the pioneering work of Garrett and Munk, the statistics of oceanic internal gravity waves has become a central subject of research in oceanography. The time evolution of the spectral energy of internal waves in the ocean can be described by a near-resonance wave turbulence equation, of quantum Boltzmann type. In this work, we provide the first rigorous mathematical study for the equation by showing the global existence and uniqueness of strong solutions.
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