Geodesic
Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 176-187

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2011-057-3
Mots-clés : 76B07, 76B15, 76B45, oscillatory integrals, water waves, surface tension, Strichartz estimates 
Spirn, Daniel; Wright, J. Douglas. Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 176-187. doi: 10.4153/CMB-2011-057-3
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