Sloshing, Steklov and corners: asymptotics of sloshing eigenvalues

Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265, Parnovski, L., Polterovich, I. and Sher, D. A. (2021) Sloshing, Steklov and corners: asymptotics of sloshing eigenvalues. Journal d'Analyse Mathématique. ISSN 0021-7670 doi: 10.1007/s11854-021-0188-x

Abstract/Summary

In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We prove a two-term asymptotic formula for sloshing eigenvalues. In particular, this confirms a conjecture posed by Fox and Kuttler in 1983. We also obtain similar eigenvalue asymptotics for other related mixed Steklov type problems, and discuss applications to the study of Steklov spectral asymptotics on polygons.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/75925
Identification Number/DOI	10.1007/s11854-021-0188-x
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer Link
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