Journal article
Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension
Canadian mathematical bulletin, v 55(1)
01 Mar 2012
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of
${{t}^{-5/6}}$
. This rate is due to competition between surface tension and gravitation at
$O(1)$
wave numbers and is connected to the fact that, in the presence of surface tension, there is a so-called “slowest wave”. Additionally, we combine our dispersive estimates with
${{L}^{2}}$
type energy bounds to prove a family of Strichartz estimates.
Metrics
Details
- Title
- Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension
- Creators
- Daniel Spirn - University of MinnesotaJ. Douglas Wright - Drexel University
- Publication Details
- Canadian mathematical bulletin, v 55(1)
- Publisher
- Cambridge University Press
- Number of pages
- 12
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000300865000021
- Scopus ID
- 2-s2.0-84865315252
- Other Identifier
- 991019182658404721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics