# The Navier-Stokes equations with initial data in uniformly local $L^{p}$ spaces

Preprint Series # 741
Maekawa, Yasunori and Terasawa, Yutaka The Navier-Stokes equations with initial data in uniformly local $L^{p}$ spaces. (2005);

 TeX DVI143Kb

## Abstract

We construct the local mild solutions of the Cauchy problem for the incompressible homogeneous Navier-Stokes equations in the $d$-dimensional Eucledian space with initial data in uniformly local $L^{p}$ (=$L^{p}_{uloc}) spaces where$ p $is larger than or equal to$d$. As an application, we show that the mild solution associated with$ L^{d}_{uloc} $almost periodic initial data at time zero becomes uniformly local almost periodic (=$ L^{\infty}-almost periodic ) in any positive time.

Item Type: Preprint 60 Recomender, Professor Tohru Ozawa Navier-Stokes equations, Cauchy problem, uniformly local (locally uniform) space. almost periodic function 76-xx FLUID MECHANICS 1044