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1. CMB 2011 (vol 55 pp. 176)

Spirn, Daniel; Wright, J. Douglas
Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension
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.

Keywords:oscillatory integrals, water waves, surface tension, Strichartz estimates
Categories:76B07, 76B15, 76B45

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