Document Type
Article
Publication Date
1-1996
Abstract
When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution operators, and adapt the center manifold theory of Chow, Lin, and Lu.
Repository Citation
Turyn, L.
(1996). A Center-Unstable Manifold Theorem for Parametrically Excited Surface Waves. SIAM Journal on Mathematical Analysis, 27 (1), 241-257.
https://corescholar.libraries.wright.edu/math/40
DOI
10.1137/0527013
