On the local solvability in Morrey spaces of the Navier–Stokes equations in a rotating frame

We prove local-in-time (non-uniform) solvability for the rotating Navier–Stokes equations in Morrey spaces M p , μ σ ( R 3 ) . These spaces contain singular and nondecaying functions which are of interest in statistical turbulence. We give an algebraic relation between the size of existence time and angular velocity Ω . The evolution of velocity u is analyzed in suitable Kato–Fujita spaces based on Morrey spaces. We show the asymptotic behavior u Ω → w in L ∞ ( 0 , T ; M p , μ σ ( R 3 ) ) as Ω → 0 , where w is the solution for the Navier–Stokes equations with the same data u 0 . Particularly, for μ = 3 − p , the solution is approximately self-similar for small | Ω | , when u 0 is homogeneous of degree − 1 .