The Navier-Stokes equations are considered in a smooth bounded domain
where and are quasiperiodic in . It means that , where and are -periodic in each argument , the being rationally independent. The authors construct the family of processes associated to these equations and prove the existence of the uniform attractor. The following estimate of the Hausdorff dimension of the attractor is obtained
where and depend of and , is the Reynolds number, and are nondimensional constants independent of . The approach of V. V. Chepyzhov and M. I. Vishik [|J. Math. Pures Appl. 73, 279-333 (1994; Zbl 0838.58021)] is used.