Well-posedness of two-dimensional hydroelastic waves with mass

We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved well-posedness without considering the mass of the elastic surface; we now consider the effect of this mass. Under the assumption that a certain integral equation is solvable, we prove well-posedness of the initial value problem for the system. We are able to demonstrate that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. The proof uses geometric dependent variables, a normalized arclength parameterization, and a small-scale decomposition in the evolution equations.