@article{10902/32722,
year = {2024},
url = {https://hdl.handle.net/10902/32722},
abstract = {In this paper we derive three new asymptotic models for a hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of a collision-free plasma in a magnetic field. The first of these models takes the form of a non-linear and non-local Boussinesq system (for the ionic density and velocity) while the second is a non-local wave equation (for the ionic density). Moreover, we derive a unidirectional asymptotic model of the latter which is closely related to the well-known Fornberg-Whitham equation. We also provide the well-posedness of these asymptotic models in Sobolev spaces. To conclude, we demonstrate the existence of a class of initial data which exhibit wave breaking for the unidirectional model.},
organization = {D.A-O is supported by the Spanish MINECO through Juan de la Cierva fellowship FJC2020-046032-I. A.D is supported by the Spanish Agencia Estatal de Investigación under Research Grant PID2020-113554GB-I00/AEI/10.13039/501100011033 and by the Junta de Castilla y León and FEDER funds (EU) under Research Grant VA193P20. R.G-B si funded by the project "Mathematical Analysis of Fluids and Applications" Grant PID2019-109348GA-I00 funded by MCIN/AEI/ 10.13039/501100011033 and acronym "MAFyA". This publication is also supported by a 2021 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. The BBVA Foundation accepts no responsibility for the opinions, statements, and contents included in the project and/or the results thereof, which are entirely the responsibility of the authors. D.A-O and R.G-B are 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 = {Nonlinear Analysis: Theory, Methods and Applications, 2024, 244, 113539},
title = {Derivation and well-posedness for asymptotic models of cold plasmas},
author = {Alonso-Orán, Diego and Durán, Angel and Granero Belinchón, Rafael},
}