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VOL. 47.1 | 2007 On the Navier-Stokes equations with initial data nondecaying at space infinity
Yasunori Maekawa, Yutaka Terasawa

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Abstract

We will consider the Cauchy problem for the incompressible homogeneous Navier-Stokes equations in the $d$-dimensional Eucledian space with initial data in uniformly local $L^p\ (L_{uloc}^{p})$ spaces where $p$ is larger than or equal to $d$. For the construction of the local mild solution of this, $L_{uloc}^{p} - L_{uloc}^{q}$ estimates for some convolution operators are important. So we explain these estimates here.

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1137.35411
MathSciNet: MR2387234

Digital Object Identifier: 10.2969/aspm/04710197

Subjects:
Primary: 35Q30, 76D05

Rights: Copyright © 2007 Mathematical Society of Japan

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