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December 2005 Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force
Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Shin'ya Matsui
Methods Appl. Anal. 12(4): 381-394 (December 2005).


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.


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Yoshikazu Giga. Katsuya Inui. Alex Mahalov. Shin'ya Matsui. "Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force." Methods Appl. Anal. 12 (4) 381 - 394, December 2005.


Published: December 2005
First available in Project Euclid: 5 April 2007

zbMATH: 1107.76023
MathSciNet: MR2258315

Primary: 28B05 , 28C05 , 76D05 , 76U05

Keywords: Coriolis Force , Navier-Stokes equations , radon measures , Riesz operators

Rights: Copyright © 2005 International Press of Boston


Vol.12 • No. 4 • December 2005
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