Dept. Math, Hokkaido Univ. EPrints Server

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);

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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
Additional Information:60 Recomender, Professor Tohru Ozawa
Uncontrolled Keywords:Navier-Stokes equations, Cauchy problem, uniformly local (locally uniform) space. almost periodic function
Subjects:76-xx FLUID MECHANICS
ID Code:1044