We study nonlinear stability of radial collapse of a cylindrical shell filled with a viscous incompressible fluid homogeneous in density. We have made the following assumptions: 1) there is a vacuum inside the shell, 2) there is the layer of compressed polytropic gas outside the shell, the gas serves as a product of instant detonation and causes nonzero constant pressure on the outer surface of the shell, 3) there is a vacuum beyond the layer of gas. By the direct Lyapunov method, we state the absolute stability of radial collapse of the viscous cylindrical shell relative to finite disturbances of the same type of symmetry. Namely, we construct a Lyapunov function satisfying all conditions of the Lyapunov first theorem (stability theorem) regardless of radial collapse mode. Thus, we confirm the Trishin hypothesis and prove that cumulation of the fluid kinetic energy during the radial collapse of the cylindrical shell near its geometric axis never originates.
|Number of pages||7|
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 16 Jul 2019|
|Event||All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019 - Novosibirsk, Russian Federation|
Duration: 13 May 2019 → 17 May 2019