TY - JOUR

T1 - On stability of radial collapse of cylindrical shell filled with viscous incompressible fluid

AU - Fursova, D. A.

AU - Gubarev, Yu G.

PY - 2019/7/16

Y1 - 2019/7/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073897624&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1268/1/012072

DO - 10.1088/1742-6596/1268/1/012072

M3 - Conference article

AN - SCOPUS:85073897624

VL - 1268

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012072

T2 - 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

Y2 - 13 May 2019 through 17 May 2019

ER -