Resumen de Interfaces in incompressible flows
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 (Cheng in Water Waves 1(1):71-130, 2019; Granero-Belinchón and Ortega in On the motion of gravity-capillary waves with odd viscosity. arXiv:2103.01062, 2021; Granero-Belinchón and Scrobogna in J Diff Equ 276:96–148 1921; SIAM J Appl Math 79(6):2530–2550, 2019; Proc Am Math Soc 148(12):5181–5191, 2020; Phys Fluids 33(10):102115, 2021; Granero-Belinchón and Shkoller in Multiscale Model Simul 15(1):274–308, 2017) together with some new results regarding the well-posedness of the resulting PDEs.
