@article{10902/35559,
year = {2025},
month = {5},
url = {https://hdl.handle.net/10902/35559},
abstract = {In this paper, we establish the global-in-time well-posedness for an arbitrary C¹,γ, 0<γ<1, initial internal periodic wave for the free boundary gravity Stokes system in two dimensions. This classical well-posedness result is complemented by a weak solvability result in the case of Cγ or Lipschitz interfaces. In particular, we show new cancellations that prevent the so-called two-dimensional Stokes paradox, despite the polynomial growth of the Stokeslet in this horizontally periodic setting. The bounds obtained in this work are exponential in time, which are in strong agreement with the growth of the solutions obtained in [22]. Additionally, these new cancellations are used to establish global-in-time well-posedness for the Stokes-transport system with initial densities in Lp for 2<p<∞. Furthermore, we also propose and analyze several one-dimensional models that capture different aspects of the full internal wave problem for the gravity Stokes system, showing that all of these models exhibit finite-time singularities. This fact evidences the fine structure of the nonlinearity in the full system, which allows the free boundary problem to be globally well-posed, while simplified versions blow-up in finite time.},
organization = {FG and ES were partially supported by the AEI grants EUR2020-112271, PID2020-114703GB-I00 and PID2022-140494NA-I00. FG was partially supported by the AEI grant RED2022-134784-T funded by MCIN/AEI/10.13039/501100011033, by the Fundación de Investigación de la Universidad de Sevilla through the grant FIUS23/0207 and acknowledges support from IMAG, funded by MICINN through the Maria de Maeztu Excellence Grant CEX2020-001105-M/AEI/10.13039/501100011033. RGB is funded by the project “Análisis Matemático Aplicado y Ecuaciones Diferenciales” Grant PID2022-141187NB-I00 funded by MCIN /AEI /10.13039/501100011033 / FEDER, UE and acronym “AMAED”. This publication is part of the project PID2022-141187NB-I00 funded by MCIN/ AEI /10.13039/501100011033.},
publisher = {Elsevier},
publisher = {Journal of Differential Equations, 2024, 428, 654-687},
title = {On the global well-posedness of interface dynamics for gravity Stokes flow},
author = {Gancedo, Francisco and Granero Belinchón, Rafael and Salguero, Elena},
}