Attractors of Navier-Stokes systems and of parabolic equations, and estimates for their dimensions

DOI10.1007/BF02112325zbMath0562.35067OpenAlexW2077213180MaRDI QIDQ1056833

Mark I. Vishik, Anatoli V. Babin

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02112325

zbMATH Keywords

attractorsquasilinear parabolic equationHausdorff dimensionestimate of dimension

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Navier-Stokes equations (35Q30) Dimension theory in general topology (54F45) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (7)

Attractors of nonlinear evolution problems with dissipation ⋮ Hausdorff and fractal dimensions of attractors for functional differential equations in Banach spaces ⋮ Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems ⋮ Inertial manifolds ⋮ On the finite dimensionality of random attractors¹ ⋮ Hausdorff dimension of a random invariant set ⋮ Fractal dimensions in fluid dynamics and their effects on the Rayleigh problem, the Burger's vortex and the Kelvin-Helmholtz instability

Cites Work

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• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• A dynamical system generated by the Navier-Stokes equations
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale

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