The Hamiltonian structure for dynamic free boundary problems

DOI10.1016/0167-2789(86)90207-1zbMath0638.58044OpenAlexW2012388828MaRDI QIDQ1099463

Debra Lewis, Richard Montgomery, Jerrold E. Marsden, Tudor S. Ratiu

Publication date: 1986

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: http://infoscience.epfl.ch/record/129456

zbMATH Keywords

Poisson bracketirrotational flowHamiltonian structures for 2- or 3-dimensional incompressible flows

Mathematics Subject Classification ID

Incompressible viscous fluids (76D99) Applications of global analysis to the sciences (58Z05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Foundations of fluid mechanics (76A02)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Hamiltonian structures and stability for rigid bodies with flexible attachments
• Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
• Stability of steady flows of perfect incompressible fluid with a free boundary
• Reduction of symplectic manifolds with symmetry
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Nonlinear stability of fluid and plasma equilibria
• Fluids and Plasmas: Geometry and Dynamics
• Gauged Lie-Poisson structures
• Conservation Laws of Free Boundary Problems and the Classification of Conservation Laws for Water Waves
• Impulse, Flow Force and Variational Principles
• Nonlinear stability analysis of stratified fluid equilibria
• The shape and stability of rotating liquid drops
• Nonlinear surface waves in closed basins
• Hamiltonian structure, symmetries and conservation laws for water waves