We consider two fluids in a 2-dimensional region: The lower fluid occupies an infinitely depth region, while the upper fluid occupies a region with a fixed upper boundary. We study the dynamics of the interface between the two fluids (interface problem) in the limit in which the interface has a space periodic profile, is close to horizontal, and has a "long wave profile". We use a Hamiltonian normal form approach to show that up to corrections of second order, the equations are approximated by two decoupled Benjamin-Ono equations.
Citation: Dario Bambusi, Simone Paleari. A couple of BO equations as a normal form for the interface problem[J]. AIMS Mathematics, 2024, 9(8): 23012-23026. doi: 10.3934/math.20241118
We consider two fluids in a 2-dimensional region: The lower fluid occupies an infinitely depth region, while the upper fluid occupies a region with a fixed upper boundary. We study the dynamics of the interface between the two fluids (interface problem) in the limit in which the interface has a space periodic profile, is close to horizontal, and has a "long wave profile". We use a Hamiltonian normal form approach to show that up to corrections of second order, the equations are approximated by two decoupled Benjamin-Ono equations.
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