On stability of a capillary liquid down an inclined plane

Mariarosaria Padula

doi:10.3934/dcdss.2013.6.1343

Article Contents

2013, Volume 6, Issue 5: 1343-1353. Doi: 10.3934/dcdss.2013.6.1343

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On stability of a capillary liquid down an inclined plane

Mariarosaria Padula¹

1.
Dipartimento di Matematica, University of Ferrara, Via Macchiavelli, 35, 44121 Ferrara

Received: November 30, 2011

Revised: January 31, 2012

Published: September 2013

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Abstract

We consider capillary laminar fluid motions on an inclined plane and study spatially periodic surface waves with fixed periodicity on the line of maximum slope $\alpha_1$ and in the horizontal direction $\alpha_2$. Actually, we provide a sufficient condition on Reynolds and Weber numbers, and on the inclination angle, named condition (C), in order that the Poiseuille flow $(v_b,p_b,\Gamma_b)$ with upper flat free boundary $\Gamma_b$ and with periodicity conditions on the plane, is nonlinearly stable. Under condition (C), the perturbed surface $\Gamma_t$ is bounded for all time, and the free boundary Poiseuille flow is stable.

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Mathematics Subject Classification: Primary: 76E99; Secondary: 76D05.

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References

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