The Cauchy problem for the NavierStokes equations with spatially almost periodic initial data
Preprint Series # 683 Giga, Yoshikazu and Mahalov, Alex and Nicolaenko, Basil The Cauchy problem for the NavierStokes equations with spatially almost periodic initial data. (2004); AbstractA unique classical solution of the Cauchy problem for the NavierStokes
equations is considered when the initial velocity is spatially almost periodic.
It is shown that the solution is always spatially almost periodic
at any time provided that the solution exists.
No restriction on the space dimension is imposed.
This fact follows from continuous dependence of the
solution with respect to initial data in uniform topology.
Similar result is also established for Cauchy problem of
the threedimensional NavierStokes
equations in a rotating frame.
