Methods and Applications of Analysis

Volume 12 (2005)

Number 4

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

Pages: 381 – 394

DOI: http://dx.doi.org/10.4310/MAA.2005.v12.n4.a2

Authors

Yoshikazu Giga

Katsuya Inui

Alex Mahalov

Shin'ya Matsui

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.

Keywords

Navier-Stokes equations; Coriolis Force; radon measures; Riesz operators

2010 Mathematics Subject Classification

28B05, 28C05, 76D05, 76U05

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