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November/December 2011 The Navier-Stokes equations and weak Herz spaces
Yohei Tsutsui
Adv. Differential Equations 16(11/12): 1049-1085 (November/December 2011).

Abstract

In this paper, we discuss the Cauchy problem for Navier-Stokes equations in homogeneous weak Herz spaces $W{\dot{K}}^\alpha_{p,q}({\mathbb{R^{\textit{n}}}})$. More precisely, we construct the solution in the class $L^\infty(0,T; W{\dot{K}}^\alpha_{p,q})$ with the initial data in $W{\dot{K}}^\alpha_{p,q}$. Further, we consider the blow-up phenomena of time-local solutions and the uniqueness of global solutions with large initial data in $W{\dot{K}}^\alpha_{p,q}$. Also, we give several embeddings of weak Herz spaces into homogeneous Besov spaces $B^{-\alpha}_{p,\infty}({\mathbb{R^{\textit{n}}}})\ (\alpha >0),$ or $bmo^{-1}({\mathbb{R^{\textit{n}}}})$.

Citation

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Yohei Tsutsui. "The Navier-Stokes equations and weak Herz spaces." Adv. Differential Equations 16 (11/12) 1049 - 1085, November/December 2011.

Information

Published: November/December 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1236.35114
MathSciNet: MR2858524

Subjects:
Primary: 35Q30, 76D05

Rights: Copyright © 2011 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.16 • No. 11/12 • November/December 2011
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