On stability of inertial collapse of shells filled with viscous fluid

Abstract

Consideration is given to problems of nonlinear stability of inertial collapse of spherical and cylindrical shells filled with a viscous incompressible fluid homogeneous in density. Using Lyapunov’s direct method, we determine: 1) the necessary and sufficient condition for stability of spherically symmetrical inertial collapse of a thick spherical shell with respect to finite disturbances of symmetry of the same type and 2) absolute stability of cylindrically symmetrical inertial collapse of a cylindrical shell relative to finite disturbances of the same symmetry.