Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity

We consider the quasi‐geostrophic equation with its principal part for in with . We show that for every initial data with and , there exists a unique solution in the class of the maximal Lorentz–Besov regularity theorem such that for with and , where . If is sufficiently small, then we may take . Notice that both classes of initial data and solutions are scaling invariant.