Initial-boundary problem of the convection of viscous weakly-compressible liquid with presence of axial symmetry. II. Stability of generalized solutions

Abstract

The study of an axially-symmetric problem on the convection of a viscous, thermally inhomogeneous, weakly compressible fluid which fills a cavity in a solid is continued. A theorem on the continuous dependence of its generalized solutions on the initial conditions and on the perturbations is proved. Bounds of exponential type are obtained which characterize the decay of the solutions (in the mean) for large values of the time.