Dept. Math, Hokkaido Univ. EPrints Server

The Cauchy problem for the Navier-Stokes equations with spatially almost periodic initial data

Preprint Series # 683
Giga, Yoshikazu and Mahalov, Alex and Nicolaenko, Basil The Cauchy problem for the Navier-Stokes equations with spatially almost periodic initial data. (2004);

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Abstract

A unique classical solution of the Cauchy problem for the Navier-Stokes 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 three-dimensional Navier-Stokes equations in a rotating frame.

Item Type:Preprint
Uncontrolled Keywords:Navier-Stokes equations, spatially almost periodic solutions, the Cauchy problem
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:818