Oscillations of a viscous fluid with an inertial free surface
Journal: Contemporary Mathematics Fundamental Directions
Year: 2025

The problem of small motions and normal oscillations of a viscous fluid is investigated. The free surface contains heavy particles of some substance. These particles do not interact with each other during the free surface oscillations, or their interaction is negligible. The original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential equation in a Hilbert space. After a detailed study of the properties of the operator coefficients, a theorem on the sol