The Strong Solution of a Class of Generalized Navier-Stokes Equations

Abstract

We study initial boundary value (lBV) problem for a class of generalized Navier-Stokes equations in L^q([0, T); L^p(Ω)). Our main tools are regularity of analytic semigroup by Stokes operator and space-time estimates. As an application we can obtain some classical results of the Navier-Stokes equations such as global classical solution of 2-dimensional Navier-Stokes equation etc.