@article{10902/24534,
year = {2021},
month = {9},
url = {http://hdl.handle.net/10902/24534},
abstract = {In this article, we consider a non-local variant of the KuramotoSivashinsky 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.},
organization = {The authors would like to express sincere gratitude to Ruben Tomlin for calling our attention to an error in our first manuscript. J.H would like to thank Vladimir Georgiev for helpful discussions, and also thank Lorenzo Brandolese and Drago¸s Iftimie for providing suggestions and comments. R.G-B was supported by the LABEX MILYON (ANR-10-LABX-0070) of Universit´e de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) and by the project “Mathematical Analysis of Fluids and Applications” with reference PID2019-109348GA-I00/AEI/10.13039/501100011033 and acronym “MAFyA” funded by Agencia Estatal de Investigación and the Ministerio de Ciencia, Innovacion y Universidades (MICIU). J.H was partially funded by the ANR project Dyficolti ANR-13-BS01-0003-01 and is supported by the Sophie Germain program of the Fondation Math´ematique Jacques Hadamard. The authors would like to thank the referee’s remarks and suggestions},
publisher = {American Institute of Mathematical Sciences},
publisher = {Discrete and Continuous Dynamical Systems - Series A, 41 (9),  4041 - 4064},
title = {On the dynamics of 3d electrified falling films},
author = {He, Jiao and Granero Belinchón, Rafael},
}