Open AccessOn stability of radial collapse of cylindrical shell filled with viscous incompressible fluid
Author(s) -
D. A. Fursova,
Yury A. Gubarev
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1268/1/012072
Subject(s) - polytropic process , shell (structure) , compressibility , mechanics , spherical shell , physics , classical mechanics , viscous liquid , detonation , nonlinear system , lyapunov function , materials science , chemistry , organic chemistry , quantum mechanics , composite material , explosive material
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.