On smooth dependence on initial conditions for dissipative PDEs, an ODE-type approach.

DOI10.1016/j.jde.2003.07.009zbMath1043.35034OpenAlexW1982884543MaRDI QIDQ1419805

Piotr Zgliczyński

Publication date: 26 January 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.07.009

zbMATH Keywords

Navier-Stokes equationsGalerkin projectionscompact attractorcompact trapping region

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Periodic solutions to PDEs (35B10) Theoretical approximation of solutions to ordinary differential equations (34A45) Navier-Stokes equations (35Q30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05)

Related Items (5)

Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations ⋮ Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof ⋮ A verified optimization technique to locate chaotic regions of Hénon systems ⋮ Convergence of Galerkin solutions and continuous dependence on data in spectrally-hyperviscous models of 3D turbulent flow ⋮ A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line

Cites Work

• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Geometric theory of semilinear parabolic equations
• Recent results on mathematical and statistical hydrodynamics
• Low-dimensional behaviour in the complex Ginzburg-Landau equation
• AN ELEMENTARY PROOF OF THE EXISTENCE AND UNIQUENESS THEOREM FOR THE NAVIER–STOKES EQUATIONS
• Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation
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