Invariant Manifolds and Their Zero-Viscosity Limits for Navier-Stokes Equations
| dc.creator | Li, Y. Charles | |
| dc.date | 2005-05-18 | |
| dc.date.accessioned | 2026-07-07T05:20:00Z | |
| dc.date.available | 2026-07-07T05:20:00Z | |
| dc.description | First we prove a general spectral theorem for the linear Navier-Stokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and higher order eigenfunctions) form a complete basis in $H^\ell$ ($\ell = 0,1,2, ...$). Then we prove the existence of invariant manifolds. We are also interested in a more challenging problem, i.e. studying the zero-viscosity limits ($ν\ra 0^+$) of the invariant manifolds. Under an assumption, we can show that the sizes of the unstable manifold and the center-stable manifold of a steady state are $O(\sqrtν)$, while the sizes of the stable manifold, the center manifold, and the center-unstable manifold are $O(ν)$, as $ν\ra 0^+$. Finally, we study three examples. The first example is defined on a rectangular periodic domain, and has only one unstable eigenvalue which is real. A complete estimate on this eigenvalue is obtained. Existence of an 1D unstable manifold and a codim 1 stable manifold is proved without any assumption. For the other two examples, partial estimates on the eigenvalues are obtained. | |
| dc.description | 28pp | |
| dc.identifier | https://arxiv.org/abs/math/0505390 | |
| dc.identifier | http://arxiv.org/abs/math/0505390 | |
| dc.identifier | Dynamics of PDE, Vol.2, No.2, (2005), 159-196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75235 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | Fluid Dynamics | |
| dc.subject | 35, 76, 37, 34 | |
| dc.title | Invariant Manifolds and Their Zero-Viscosity Limits for Navier-Stokes Equations | |
| dc.type | text |