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On the dynamics of 3D electrified falling films

Jiao He 1 Rafael Granero-Belinchón 1
1 EDPA - Équations aux dérivées partielles, analyse
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing the global wellposedness of this equation we also obtain some qualitative properties of the solutions. In particular, we prove that the solutions become analytic in the spatial variable for positive time, the existence of a compact global attractor and an upper bound on the number of spatial oscillations of the solutions. We observe that such a bound is particularly interesting due to the chaotic behavior of the solutions.
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https://hal.archives-ouvertes.fr/hal-02168399
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Submitted on : Tuesday, November 10, 2020 - 5:11:52 PM
Last modification on : Monday, November 16, 2020 - 9:11:22 AM

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  • HAL Id : hal-02168399, version 2

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Jiao He, Rafael Granero-Belinchón. On the dynamics of 3D electrified falling films. 2020. ⟨hal-02168399v2⟩

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