The Navier-Stokes Equations

Part 1 Flow in bounded and unbounded domains: a Reynolds equation derived from the micropolar Navier-Stokes system more Lyapunov functions for the Navier-Stokes equation on the nonlinear stability of the magnetic Benard problem stability of Navier-Stokes flows through permeable boundaries on steady solutions of the Kuramoto-Sivashinsky equation classical solutions to the stationary Navier-Stokes system in exterior domains stationary Navier-Stokes flow in two-dimensional Y-shape channel under general outflow condition regularity of solutions to the Stokes equations under a certain nonlinear boundary condition viscous incompressible flow in unbounded domains lifespan and global existence of 2-D compressible fluids on the theory of nonstationary hyrrodynamic potentials a note on the blow-up criterion for the inviscid 2-D Boussinesq equations weak solutions to viscous heat-conducting gas 1D-equations with discontinuous data - global existence, uniqueness, and regularity. Part 2 General qualitative theory: regularity criteria of the axisymmetric Navier-Stokes equations. (Part contents).