Applied Physics and Mathematics Annotation << Back ABOUT DYNAMICAL COMPRESSION (EXPANSION) OF SPHERICAL LAYER IN VISCOUS INCOMPRESSIBLE FLUID. ZABABAXIN PROBLEM А.B. KISELEV In paper present precise analytical solution for onedimensional dynamical problem of compression (extension) of spherical layer from incompressible viscous fluid Navier- Stokes type. Motion of fluid layer in initial time moment is absent and on external and internal its surfaces act pressures, which depends on time as arbitrary functions. Solutions obtained in Lagrangian coordinates. In case then external boundary of liquid layer recede to infinity and pressure into cavity (bubble) is equal zero (Zababaxin problem) we show that for any initial radius of bubble its filling of liquid always take place on infinite time. Moreover then radius of bubble strive to zero its time of collapse strive to finite value which depends only of ratio of dynamic viscosity and pressure on infinity. Velocity of small bubbles filling strive to zero. These solutions, in particular, can be used for testing new programs of computing calculations and for estimate of effectiveness of numerical methods. Key words: spherical layer of viscous fluid Navier-Stocks type, incompressibility. Contacts: Е-mail: akis2006@yandex.ru Pp. 15-19.