A Hamiltonian approach for nonlinear rotational capillary-gravity water waves in stratified flows

Calin Iulian Martin

doi:10.3934/dcds.2017016

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2017, Volume 37, Issue 1: 387-404. Doi: 10.3934/dcds.2017016

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A Hamiltonian approach for nonlinear rotational capillary-gravity water waves in stratified flows

Calin Iulian Martin^,

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

* Corresponding author: Calin Iulian Martin
* Corresponding author: Calin Iulian Martin

Received: February 29, 2016

Revised: April 30, 2016

Published: September 2017

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Abstract

Under consideration here are two-dimensional rotational stratified water flows driven by gravity and surface tension, bounded below by a rigid flat bed and above by a free surface. The distribution of vorticity and of density is piecewise constant-with a jump across the interface separating the fluid of bigger density from the lighter fluid adjacent to the free surface. The main result is that the governing equations for the two-layered rotational stratified flows, as described above, admit a Hamiltonian formulation.

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Mathematics Subject Classification: Primary:35Q31, 35Q35, 76B15, 76D45;Secondary:76D33.

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