Global well-posedness and ill-posedness for the Navier-Stokes equations with the Coriolis force in function spaces of Besov type

摘要

We consider the initial value problems for the Navier-Stokes equations in the rotational framework. We introduce function spaces B_(p,q)~s(R~3) of Besov type, and prove the global in time existence and the uniqueness of the mild solution for small initial data in our space B_(1,2)~(-1)(R~3) near BMO~(-1)(R~3). Furthermore, we also discuss the ill-posedness for the Navier-Stokes equations with the Coriolis force, which implies the optimality of our function space B_(1,2)~(-1)(R~3) for the global well-posedness.