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arXiv · 2112.15229

Interfaces in incompressible flows

Rafael Granero-Belinchón
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Abstract

The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular, we review the derivation of some new models describing the dynamics of gravity-capillary nonlinear waves in incompressible flows. These models take the form of both bidirectional and unidirectional nonlinear and nonlocal wave equations. More precisely, with the goal of telling a more complete story, in this paper we present the results in the works \cite{GS,aurther2019rigorous,granero2019models,granero2019well,granero2020well,granero2021motion, granero2021global} together with some new results regarding the well-posedness of the resulting PDEs.

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Rafael Granero-Belinchón. 2021-12-30. Interfaces in incompressible flows. https://arxiv.org/abs/2112.15229

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