Uniform local solvability for the Navier-Stokes equations with the Coriolis force
Preprint Series # 736
Giga, Yoshikazu and Inui, Katsuya and Mahalov, Alex and Matsui, Shin'ya Uniform local solvability for the Navier-Stokes equations with the Coriolis force. (2005);
The unique local existence is established for the Cauchy problem of the incompressible Navier-Stokes equations with the Coriolis force. 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 data as Fourier preimage of the space of all finite Radon measures with no point mass at the origin we prove uniform estimate for the existence time in the speed of rotation.