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International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 9, Pages 587-602

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

Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 117234, Russia

Received 23 March 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.