Abstract
We consider the initial value problems for the Navier–Stokes equations in the rotational framework. We introduce function spaces B˙p,qs(R3) 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(R3) near BMO−1(R3). 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(R3) for the global well-posedness.
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