# Radiation conditions at the top of a rotational cusp in the theory of water-waves

Sergey A. Nazarov; Jari Taskinen

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 5, page 947-979
- ISSN: 0764-583X

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topNazarov, Sergey A., and Taskinen, Jari. "Radiation conditions at the top of a rotational cusp in the theory of water-waves." ESAIM: Mathematical Modelling and Numerical Analysis 45.5 (2011): 947-979. <http://eudml.org/doc/197567>.

@article{Nazarov2011,

abstract = {
We study the linearized water-wave problem in a bounded domain (e.g. a
finite pond of water) of $\{\mathbb R\}^3$, having a cuspidal boundary
irregularity created by a submerged body. In earlier publications the
authors discovered that
in this situation the spectrum of the problem may contain a
continuous component in spite of the boundedness of the domain.
Here, we proceed to impose and study radiation conditions at a point $\{\mathcal O\}$
of the water surface, where
a submerged body touches the surface
(see Fig. 1). The radiation conditions emerge from the requirement that
the linear operator associated to the problem be Fredholm of index zero
in relevant weighted function spaces with separated asymptotics.
The classification
of incoming and outgoing (seen from $\{\mathcal O\}$) waves
and the unitary scattering matrix are introduced.
},

author = {Nazarov, Sergey A., Taskinen, Jari},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Linear water-wave problem; cuspidal domain; radiation condition; scattering matrix; linear water-wave problem},

language = {eng},

month = {5},

number = {5},

pages = {947-979},

publisher = {EDP Sciences},

title = {Radiation conditions at the top of a rotational cusp in the theory of water-waves},

url = {http://eudml.org/doc/197567},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Nazarov, Sergey A.

AU - Taskinen, Jari

TI - Radiation conditions at the top of a rotational cusp in the theory of water-waves

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/5//

PB - EDP Sciences

VL - 45

IS - 5

SP - 947

EP - 979

AB -
We study the linearized water-wave problem in a bounded domain (e.g. a
finite pond of water) of ${\mathbb R}^3$, having a cuspidal boundary
irregularity created by a submerged body. In earlier publications the
authors discovered that
in this situation the spectrum of the problem may contain a
continuous component in spite of the boundedness of the domain.
Here, we proceed to impose and study radiation conditions at a point ${\mathcal O}$
of the water surface, where
a submerged body touches the surface
(see Fig. 1). The radiation conditions emerge from the requirement that
the linear operator associated to the problem be Fredholm of index zero
in relevant weighted function spaces with separated asymptotics.
The classification
of incoming and outgoing (seen from ${\mathcal O}$) waves
and the unitary scattering matrix are introduced.

LA - eng

KW - Linear water-wave problem; cuspidal domain; radiation condition; scattering matrix; linear water-wave problem

UR - http://eudml.org/doc/197567

ER -

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