Semigroup characterization of Besov type Morrey spaces and well-posedness of generalized Navier–Stokes equations

The well-posedness of generalized Navier–Stokes equations with initial data in some critical homogeneous Besov spaces and in some critical Q spaces was known. In this paper, we establish a wavelet characterization of Besov type Morrey spaces under the action of semigroup. As an application, we obtain the well-posedness of smooth solution for the generalized Navier–Stokes equations with initial data in some critical homogeneous Besov type Morrey spaces (, γ1−γ2=1−2β), 1