On the dynamics of 3D electrified falling films

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jun 2019 Spain Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete and Continuous Dynamical Systems, volume 41, pages 4,041-4,064 (issn: 1078-0947, eissn: 1553-5231,

Copyright policy )Funded by:ANR | MILYON, ANR | Avenir L.S.E., ANR | DYFICOLTI

Authors: He, Jiao; Granero Belinchón, Rafael;

doi: 10.3934/dcds.2021027 , 10.48550/arxiv.1906.12205

arXiv: 1906.12205

handle: 10902/24534

On the dynamics of 3D electrified falling films

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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.

Country

Spain

Related Organizations

University of Cantabria
Spain
University of Évry Val d'Essonne
France

Keywords

Kuramoto-Sivashinsky equation, Analyticity, Upper bound on the number of spatial oscillations, global attractor, PDEs in connection with fluid mechanics, analyticity, Global attractor, Global wellposedness, Mathematics - Analysis of PDEs, upper bound on the number of spatial oscillations, FOS: Mathematics, Attractors, Initial-boundary value problems for higher-order parabolic equations, global wellposedness, Semilinear parabolic equations, Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems, periodic boundary conditions, Analysis of PDEs (math.AP)

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