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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