Swaters, Gordon E

"…a refreshingly non-technical style…this is a well-written introduction to Hamiltonian fluid dynamics and basic stability results."--S. Reich, Edinburgh Mathematical Society, Vol. 44

• Introduction The Nonlinear Pendulum Model Formulation Canonical Hamiltonian Formulation Least Action Principle Symplectic Hamiltonian Formulation Mathematical Properties of the J Matrix Poisson Bracket Formulation Steady Solutions of a Canonical Hamiltonian System Linear Stability of a Steady Solution Nonlinear Stability of a Steady Solution The Two Dimensional Euler Equations Vorticity Equation Formulation Hamiltonian Structure for Partial Differential Equations Hamiltonian Structure of the Euler Equations Reduction of the Canonical Poisson Bracket Casimir Functionals and Noether's Theorem Exercises Stability of Steady Euler Flows Steady Solutions of the Vorticity Equation Linear Stability Problem Normal Mode Equations for Parallel Shear Flows Linear Stability Theorems Nonlinear Stability Theorems Andrews' Theorem Flows with Special Symmetries Exercises The Charney-Hasegawa-Mima Equation A Derivation of the CHM Equation Hamiltonian Structure Steady Solutions Stability of Steady Solutions Steadily-Travelling Solutions Exercises The KdV Equation A Derivation of the KdV Equation Hamiltonian Structure Periodic and Soliton Solutions Variational Principles Linear Stability Nonlinear Stability Exercises

Swaters, Gordon E

"…a refreshingly non-technical style…this is a well-written introduction to Hamiltonian fluid dynamics and basic stability results."--S. Reich, Edinburgh Mathematical Society, Vol. 44

• Introduction The Nonlinear Pendulum Model Formulation Canonical Hamiltonian Formulation Least Action Principle Symplectic Hamiltonian Formulation Mathematical Properties of the J Matrix Poisson Bracket Formulation Steady Solutions of a Canonical Hamiltonian System Linear Stability of a Steady Solution Nonlinear Stability of a Steady Solution The Two Dimensional Euler Equations Vorticity Equation Formulation Hamiltonian Structure for Partial Differential Equations Hamiltonian Structure of the Euler Equations Reduction of the Canonical Poisson Bracket Casimir Functionals and Noether's Theorem Exercises Stability of Steady Euler Flows Steady Solutions of the Vorticity Equation Linear Stability Problem Normal Mode Equations for Parallel Shear Flows Linear Stability Theorems Nonlinear Stability Theorems Andrews' Theorem Flows with Special Symmetries Exercises The Charney-Hasegawa-Mima Equation A Derivation of the CHM Equation Hamiltonian Structure Steady Solutions Stability of Steady Solutions Steadily-Travelling Solutions Exercises The KdV Equation A Derivation of the KdV Equation Hamiltonian Structure Periodic and Soliton Solutions Variational Principles Linear Stability Nonlinear Stability Exercises