Regularity Of Mild Solution For Navier - Stokes Equations

Navier-Stokes equations are the equations describing the viscous Newton fluid in fluid mechanics. They have very important significance for solving practical problems. The solutions to the Navier-Stokes equations can explain and predict the law of motion of viscous Newton fluid. Due to the nonlinearity of the Navier-Stokes equations, we usually study solutions to the Navier-Stokes equations in the sense of distribution, namely, weak solution. The weak solutions to the Navier-Stokes equations are classical solutions when the weak solutions are smooth enough. The Navier-Stokes equation with the Coriolis force describe the motion of fluid under the rotational framework. On the earth, relative to the motion of the earth, objects will be subjected to inertia force, known for Coriolis force. After the introduction of the Coriolis force, people can simply deal with the motion equation in a rotating system. We study the regularity of the mild solution to the Navier-Stokes equations in BC (R; Lγσ (R3))∩BC (R; W1q (R3)). We prove the regularity of the tim periodic mild solutions to the Navier Stokes equations with Coriolis force when the external force belongs to BC (R; Bp,2-s(R3)) ∩ BC (R; Ll (R3)).