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2007 Global solvability of the Navier-Stokes equations in spaces based on sum-closed frequency sets
Yoshikazu Giga, Katsuya Inui, Alex Mahalov, Jürgen Saal
Adv. Differential Equations 12(7): 721-736 (2007).

Abstract

We prove existence of global regular solutions for the $3$D Navier-Stokes equations with (or without) Coriolis force for a class of initial data $u_0$ in the space ${{{\mathrm{FM}}}_{\sigma,\delta}}$, i.e., for functions whose Fourier image ${\widehat{u}}_0$ is a vector-valued Radon measure and that are supported in sum-closed frequency sets with distance $\delta$ from the origin. In our main result we establish an upper bound for admissible initial data in terms of the Reynolds number, uniform on the Coriolis parameter $\Omega$. In particular this means that this upper bound is linearly growing in $\delta$. This implies that we obtain global-in-time regular solutions for large (in norm) initial data $u_0$ which may not decay at space infinity, provided that the distance $\delta$ of the sum-closed frequency set from the origin is sufficiently large.

Citation

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Yoshikazu Giga. Katsuya Inui. Alex Mahalov. Jürgen Saal. "Global solvability of the Navier-Stokes equations in spaces based on sum-closed frequency sets." Adv. Differential Equations 12 (7) 721 - 736, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1144.76009
MathSciNet: MR2331521

Subjects:
Primary: 35Q30
Secondary: 76D03, 76D05, 76U05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 7 • 2007
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