Uniqueness of weak solutions to the limit resonant equation of 3D rotating Navier-Stokes equations

Abstract

The limit resonant equation of the 3D rotating Navier-Stokes equations is obtained by taking large rotation limit. This equation has a nonlinear term with restricted interactions between Fourier modes, and thus it enjoys better regularity estimates than those of the classical 3D Navier-Stokes equations. Such estimates enable us to prove uniqueness of weak solutions to the limit resonant equation.