The Navier-Stokes Equations Theory and Numerical Methods Lecture Notes in Pure and Applied Mathematics Series

"Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."

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).

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Rodolfo Salvi