Generalized Navier–Stokes equations with initial data in local Q-type spaces

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier–Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of Q α , loc β , − 1 ( R 3 ) . This result applies to the usual incompressible Navier–Stokes equations.