Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 7, Number 3 (2009), 521-547.
Linear dispersive decay estimates for vortex sheets with surface tension
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 $t^−1/3$
Commun. Math. Sci., Volume 7, Number 3 (2009), 521-547.
First available in Project Euclid: 26 October 2009
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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