Uniform local solvability for the NavierStokes 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 NavierStokes equations with the Coriolis force. (2005); AbstractThe unique local existence is established for the Cauchy problem of the incompressible NavierStokes equations with the Coriolis force. The Coriolis operator restricted to divergence free vector fields is a zero order pseudodifferential operator with the skewsymmetric matrix symbol related to the Riesz operator. It leads to the additional term in the NavierStokes 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.
