Accession Number:

ADA061526

Title:

A Stability Investigation for an Incompressible Simple Fluid with Fading Memory,

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s):

• Infante,E. F.
• Walker,J. A.

Report Date:

1978-08-01

Pagination or Media Count:

27.0

Abstract:

The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the finite-linear viscoelastic theory for materials with fading memory this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several stability and asymptotic behavior results for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamic system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid. Author

Descriptors:

• *EQUATIONS OF MOTION
• *VISCOELASTICITY
• *INCOMPRESSIBLE FLOW
• STABILITY
• ENERGY
• BOUNDARY VALUE PROBLEMS
• NONLINEAR ANALYSIS
• HILBERT SPACE
• LYAPUNOV FUNCTIONS
• TENSOR ANALYSIS

Subject Categories:

• Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE