Abstract
We study initial-boundary value problem for an equation of composite type in 3-D multiply connected domain. This equation governs nonsteady inertial waves in rotating fluids. The solution of the problem is obtained in the form of dynamic potentials, which density obeys the uniquely solvable integral equation. Thereby the existence theorem is proved. Besides, the uniqueness of the solution is studied. All results hold for interior domains and for exterior domains with appropriate conditions at infinity.