Integrability and regularity of 3D Euler and equations for uniformly rotating fluids (Q1921217)

The authors consider the periodic solutions of the classical Euler equations for incompressible fluids with the additional term \(2\Omega JU\) in the equation of dynamics. This Coriolis force term is responsible for uniform rotation of fluids. It is shown that solutions can be decomposed into three summands, the first one is a solution of the two-dimensional Euler system with vertically averaged initial data, the second one is related to a solution of a new system, and the third summand is a remainder of the \(\text{Ro}^{1/2}\) order where Ro is with the anisotropic Rossby number Ro. A number of theorems for sufficiently smooth initial data are claimed without proof, including existence of regular solutions on the time interval depending on the Rossby number. This interval goes to infinity as \(\text{Ro}\to 0\).