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 Pavel A. Krutitskii. 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.