Communications in Mathematical Sciences

Linear dispersive decay estimates for vortex sheets with surface tension

Daniel Spirn and J. Douglas Wright

Full-text: Open access

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 $t^−1/3$

Article information

Source
Commun. Math. Sci., Volume 7, Number 3 (2009), 521-547.

Dates
First available in Project Euclid: 26 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.cms/1256562811

Mathematical Reviews number (MathSciNet)
MR2569021

Zentralblatt MATH identifier
1186.35167

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 76B45: Capillarity (surface tension) [See also 76D45] 76B47: Vortex flows 76B07: Free-surface potential flows 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 35B45: A priori estimates

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

Citation

Spirn, Daniel; Wright, J. Douglas. Linear dispersive decay estimates for vortex sheets with surface tension. Commun. Math. Sci. 7 (2009), no. 3, 521--547. https://projecteuclid.org/euclid.cms/1256562811


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