The NavierStokes equations with initial data in uniformly local $ L^{p} $ spaces
Preprint Series # 741 Maekawa, Yasunori and Terasawa, Yutaka The NavierStokes equations with initial data in uniformly local $ L^{p} $ spaces. (2005); AbstractWe construct the local mild solutions of the Cauchy problem for the incompressible homogeneous NavierStokes 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:  NavierStokes equations, Cauchy problem, uniformly local (locally uniform) space. almost periodic function 

Subjects:  76xx FLUID MECHANICS 

ID Code:  1044 

