Communications in Mathematical Sciences

Volume 7 (2009)

Number 3

Linear dispersive decay estimates for vortex sheets with surface tension

Pages: 521 – 547

DOI: http://dx.doi.org/10.4310/CMS.2009.v7.n3.a1

Authors

Daniel Spirn

J. Douglas Wright

Abstract

We consider the amplitude decay for the linearized equations governing irrotational vortex sheets and water waves with surface tension. Using oscillatory integral estimates, we prove that the magnitude of the amplitude decays faster than $t^−1/3$

Keywords

Water waves; surface tension; vortex sheets; oscillatory integrals; dispersive estimates; Strichartz estimates

2010 Mathematics Subject Classification

35B45, 35Q35, 76B07, 76B15, 76B45, 76B47

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