Methods and Applications of Analysis

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

Yoshikazu Giga, Katsuya Inui, Alex Mahalov, and Shin'ya Matsui

Full-text: Open access

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.

Article information

Source
Methods Appl. Anal., Volume 12, Number 4 (2005), 381-394.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.maa/1175797465

Mathematical Reviews number (MathSciNet)
MR2258315

Zentralblatt MATH identifier
1107.76023

Subjects
Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76U05: Rotating fluids 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 28C05: Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures

Keywords
Navier-Stokes equations Coriolis Force radon measures Riesz operators

Citation

Giga, Yoshikazu; Inui, Katsuya; Mahalov, Alex; Matsui, Shin'ya. Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force. Methods Appl. Anal. 12 (2005), no. 4, 381--394. https://projecteuclid.org/euclid.maa/1175797465


Export citation