Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

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 two-dimensional sloshing problem, which a mixed Steklov—Neumann boundary value problem describing small vertical oscillations of ideal fluid in container or canal uniform cross-section. We prove two-term asymptotic formula eigenvalues. particular, this confirms conjecture posed by Fox and Kuttler 1983. also similar eigenvalue other related problems, discuss applications study polygons.