Almost Periodic Mild Solutions Of Navier-Stokes Equation With Coriolis Force

Navier-Stokes equations are a class of important equations in the theory of partial differential equations. The existence, uniqueness, regularity, stability and periodicity of the solution to this kind of equations were studied by many researchers such as Leray, Lions, Serrin, Nirenberg, Caffarelli, etc. The study on the periodicity of solutions to Navier-Stokes equation is also interesting to researchers. As we knew, it is an idealized method to simulate data from the practical problem by the periodic functions. And this simulation might cause big errors. However, this kind of problem can be solved prop-erly by the theory of almost periodic function proposed by Harald Bohr when studying Dirichlet series. In the theory of partial differential equation, it's very important topic to study almost periodicity of the solution to equation. In this paper, we study almost periodic solutions to Navier-Stokes equation. We prove that there exists unique almost periodic mild solution in BUC(R?L?r(R3))?BUC(R?W1,q(R3)) for three dimensional incompressible Navier-Stokes equation with the Coriolis force with almost periodic free term f; and in Fourier-Besov spaces, we also show that there holds unique almost peri-odic solution in BC (R;FBp,r2-3/p(R3)) under certain condition for the almost periodic function f.