The Strong Solution of a Class of Generalized Navier-Stokes Equations (Journal of Partial Differential Equations, 2000)
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.
Keywords: Admissible triple; generalized Navier-Stokes equations; i nitial boundary value problem; space-time estimates