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

Sergey A. Nazarov;  Jari Taskinen — 2011

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the linearized water-wave problem in a bounded domain (a finite pond of water) of 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 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...

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

Sergey A. Nazarov;  Jari Taskinen — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We study the linearized water-wave problem in a bounded domain ( a finite pond of water) of 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 𝒪 of the water surface, where a submerged body touches the surface (see Fig. 1). The...

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