Interfaces in incompressible flows

Granero-Belinchón, Rafael

doi:10.1007/s40324-021-00283-w

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2022

2024

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Cited by 3 publications

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“…Furthermore, this is also a first principles step towards the description of viscous water waves. Indeed, although for most of the applications in coastal engineering, water waves are assumed to be inviscid, as already stated by the celebrated applied mathematician Longuet-Higgins [35] (see [20] for more details regarding the mathematical modeling of viscous waves):…”

Section: Introductionmentioning

confidence: 99%

Long time interface dynamics for gravity Stokes flow

Gancedo¹,

Granero-Belinchón²,

Salguero³

2022

Preprint

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We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravity force and the density difference induces the dynamics of the interface. We derive the contour dynamics formulation for this problem through a x 1 -periodic version of the Stokeslet. Using this new system, we show local-in-time well-posedness when the initial interface is described by a curve with no selfintersections and C 1+γ Hölder regularity, 0 < γ < 1. Global-in-time stability to the flat stationary state is proved in the Rayleigh-Taylor stable regime for small initial data in Sobolev spaces.

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Section: Introductionmentioning

confidence: 99%