R Boundedness, Maximal Regularity and Free Boundary Problems for the Navier Stokes Equations

摘要

3.1 Introduction 3.1.1 Free Boundary Problem for the Navier-Stokes Equations In this chapter, we study free boundary problem for the Navier-Stokes equations, and R bounded solution operators and L_p-L_q maximal regularity theorem for the Stokes equations with free boundary conditions. Typical problem for the free boundary problem of the Navier-Stokes equations are (P1) the motion of an isolated liquid mass and (P2) the motion of a viscous incompressible fluid contained in an ocean of infinite extent.