Navier-Stokes Equations in Planar Domains

Abstract

Basic Theory: Introduction Existence and Uniqueness of Smooth Solutions Estimates for Smooth Solutions Extension of the Solution Operator Measures as Initial Data Asymptotic Behavior for Large Time Some Theorems from Functional Analysis Approximate Solutions: Introduction Notation Finite Difference Approximation to Second-Order Boundary-Value Problems From Hermitian Derivative to the Compact Discrete Biharmonic Operator Polynomial Approach to the Discrete Biharmonic Operator Compact Approximation of the Navier - Stokes Equations in Streamfunction Formulation Fully Discrete Approximation of the Navier - Stokes Equations Numerical Simulations of the Driven Cavity Problem.