Solution of the problem of dynamics of highly viscous, incompressible media and its application to modeling the stess-strain state of the Earth's tectonosphere

Abstract

The fundamental system of dynamic equations that describe highly viscous, homogeneous incompressible media has been solved. This allows us to make the transition from the non-uniform system of equations to the calculation of integrals of a certain type under rather general restrictions on the character of distribution of external forces. As an example, an analytical solution has been found for the problem of deformations and stresses in tectonosphere caused by the action of a viscous, abnormal in density, inclusion (in the form of polyhedron) in the Earth's gravitational field. The medium and inclusion are assumed be of identical viscosity, which restricts the applicability of the obtained results, but does not lessen their theoretical importance.