Fractal dimension of attractors for viscous incompressible fluid flows

Journal Article · Mon Sep 01 04:00:00 EDT 1986 · SIAM J. Math. Anal.; (United States)

DOI:https://doi.org/10.1137/0517080· OSTI ID:6845522

Ghidaglia, J M

Generalized Navier-Stokes equations (NSE), in concert with the concepts of a functional invariant set and a strange attractor, are used to show that attractors have finite fractal dimensions and lie in a set of regular functions. Consideration is given to both homogeneous and inhomogeneous boundary conditions for the NSE, as well as the existence and uniqueness of solutions for the NSE. The proofs are carried out in Hilbert space. A squeezing property is demonstrated for the flow of strong solutions and a regularity-like property is proven for functional invariant sets and atractors. Bounded invariant sets are then confirmed to have finite fractal dimensions. Applications of the theory are illustrated through solutions to the NSE on a Riemann manifold, for thermodynamic equations and for MHD equations. 33 references.

• Research Organization: Paris XI Universite, Orsay, France
• OSTI ID: 6845522
• Journal Information: SIAM J. Math. Anal.; (United States), Journal Name: SIAM J. Math. Anal.; (United States) Vol. 17; ISSN SJMAA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BANACH SPACE
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
FLUID MECHANICS
HILBERT SPACE
HYDRODYNAMICS
INCOMPRESSIBLE FLOW
MAGNETOHYDRODYNAMICS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
VISCOUS FLOW