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We study initial-boundary value problem for an equation ofcomposite type in 3-D multiply connected domain. This equationgoverns nonsteady inertial waves in rotating fluids. The solutionof the problem is obtained in the form of dynamic potentials, whichdensity obeys the uniquely solvable integral equation. Thereby theexistence theorem is proved. Besides, the uniqueness of thesolution is studied. All results hold for interior domains and forexterior domains with appropriate conditions at infinity

Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition