Variational Principles for Water Waves

Boris Kolev (1) , David Sattinger (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Université de Yale

We describe the Hamiltonian structures, including the Poisson brackets and Hamiltonians, for free boundary problems for incompressible fluid flows with vorticity. The Hamiltonian structure is used to obtain variational principles for stationary gravity waves both for irrotational flows as well as flows with vorticity.

Mots clés: water waves; variational principles; Poisson structures

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Boris Kolev, David Sattinger. Variational Principles for Water Waves. SIAM Journal on Mathematical Analysis, 2006, 38 (3), pp. 906-920. ⟨10.1137/050647220⟩. ⟨hal-00117607⟩