Global Solutions of the Navier]Stokes Equations in Thin Three-Dimensional Domains

This paper is concerned with the spatially periodic Navier]Stokes equations in a thin three-dimensional domain. It is shown that the classical solution exists globally when the initial velocity u0 and the external force f are chosen in the set significantly larger than those presented in earlier works. What is more, it is shown that these global solutions, which seem large in a function space, are small in nature.