Persistence of Invariant Manifolds for Nonlinear PDEs

DOI10.1111/1467-9590.00103zbMath1002.37037arXivmath/9807090OpenAlexW2086938482MaRDI QIDQ4784656

Don A. Jones, Steve Shkoller

Publication date: 11 December 2002

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9807090

zbMATH Keywords

stabilitysmoothingtwo-dimensional Navier-Stokes equationhyperbolic fixed pointsglobal unstable manifoldsinfinite-dimensional Hilbert manifold

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear differential equations in abstract spaces (34G20) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25) Qualitative properties of solutions to partial differential equations (35B99)

Related Items

The Role of SE ( d ) $$\mathop{\mathrm{SE}}\nolimits (d)$$ -Reduction for Swimming in Stokes and Navier-Stokes Fluids, Persistence of a normally hyperbolic manifold for a system of non densely defined Cauchy problems, Time dependent center manifold in PDEs, Approximative dichotomy and persistence of nonuniformly normally hyperbolic invariant manifolds in Banach spaces, Perturbations of normally hyperbolic manifolds with applications to the Navier-Stokes equations, Modified-truncation finite difference schemes, A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities, Persistence of invariant sets for dissipative evolution equations