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.
@article{1175797465,
author = {Giga, Yoshikazu and Inui, Katsuya and Mahalov, Alex and Matsui, Shin'ya},
title = {Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force},
journal = {Methods Appl. Anal.},
volume = {12},
number = {1},
year = {2005},
pages = { 381-394},
language = {en},
url = {http://dml.mathdoc.fr/item/1175797465}
}
Giga, Yoshikazu; Inui, Katsuya; Mahalov, Alex; Matsui, Shin'ya. Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force. Methods Appl. Anal., Tome 12 (2005) no. 1, pp. 381-394. http://gdmltest.u-ga.fr/item/1175797465/