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2006 The Navier-Stokes equations with initial data in uniformly local $L^p$ spaces
Yasunori Maekawa, Yutaka Terasawa
Differential Integral Equations 19(4): 369-400 (2006).

Abstract

In this paper we will construct local mild solutions of the Cauchy problem for the incompressible homogeneous Navier-Stokes equations in $d$-dimensional Euclidian space with initial data in uniformly local $ L^{p} $ ($ L^{p}_{uloc}$) spaces where $ p $ is greater than or equal to $d$. For the proof, we shall establish $L^p_{uloc}-L^q_{uloc}$ estimates for some convolution operators. We will also show that the mild solution associated with $ L^{d}_{uloc} $ almost periodic initial data at time zero becomes uniformly local almost periodic ($L^{\infty}$-almost periodic ) in any positive time.

Citation

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Yasunori Maekawa. Yutaka Terasawa. "The Navier-Stokes equations with initial data in uniformly local $L^p$ spaces." Differential Integral Equations 19 (4) 369 - 400, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35350
MathSciNet: MR2215625

Subjects:
Primary: 35Q30
Secondary: 35B15 , 76D03

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 4 • 2006
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