Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force

Abstract

The unique local existence is established for the Cauchy problem of the incompressible Navier-Stokes equations with the Coriolis force for a class of initial data nondecreasing at space infinity. The Coriolis operator restricted to divergence free vector fields is a zero order pseudodifferential operator with the skew-symmetric matrix symbol related to the Riesz operator. It leads to the additional term in the Navier-Stokes equations which has real parameter being proportional to the speed of rotation. For initial datum as Fourier preimage of finite Radon measures having no-point mass at the origin we show that the length of existence time-interval of mild solution is independent of the rotation speed.