Local existence of solutions to the transient quantum hydrodynamic equations

The existence of weak solutions locally in time to the quantum hydrodynamic equations in bounded domains is shown. These Madelung-type equations consist of the Euler equations, including the quantum Bohm potential term, for the particle density and the particle current density and are coupled to the...

Descripción completa

Detalles Bibliográficos
Autores principales: Jüngel, A., Mariani, M.C., Rial, D.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p485_Jungel
Aporte de:
id todo:paper_02182025_v12_n4_p485_Jungel
record_format dspace
spelling todo:paper_02182025_v12_n4_p485_Jungel2023-10-03T15:10:48Z Local existence of solutions to the transient quantum hydrodynamic equations Jüngel, A. Mariani, M.C. Rial, D. The existence of weak solutions locally in time to the quantum hydrodynamic equations in bounded domains is shown. These Madelung-type equations consist of the Euler equations, including the quantum Bohm potential term, for the particle density and the particle current density and are coupled to the Poisson equation for the electrostatic potential. This model has been used in the modeling of quantum semiconductors and superfluids. The proof of the existence result is based on a formulation of the problem as a nonlinear Schrödinger-Poisson system and uses semigroup theory and fixed-point techniques. Fil:Mariani, M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rial, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p485_Jungel
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The existence of weak solutions locally in time to the quantum hydrodynamic equations in bounded domains is shown. These Madelung-type equations consist of the Euler equations, including the quantum Bohm potential term, for the particle density and the particle current density and are coupled to the Poisson equation for the electrostatic potential. This model has been used in the modeling of quantum semiconductors and superfluids. The proof of the existence result is based on a formulation of the problem as a nonlinear Schrödinger-Poisson system and uses semigroup theory and fixed-point techniques.
format JOUR
author Jüngel, A.
Mariani, M.C.
Rial, D.
spellingShingle Jüngel, A.
Mariani, M.C.
Rial, D.
Local existence of solutions to the transient quantum hydrodynamic equations
author_facet Jüngel, A.
Mariani, M.C.
Rial, D.
author_sort Jüngel, A.
title Local existence of solutions to the transient quantum hydrodynamic equations
title_short Local existence of solutions to the transient quantum hydrodynamic equations
title_full Local existence of solutions to the transient quantum hydrodynamic equations
title_fullStr Local existence of solutions to the transient quantum hydrodynamic equations
title_full_unstemmed Local existence of solutions to the transient quantum hydrodynamic equations
title_sort local existence of solutions to the transient quantum hydrodynamic equations
url http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p485_Jungel
work_keys_str_mv AT jungela localexistenceofsolutionstothetransientquantumhydrodynamicequations
AT marianimc localexistenceofsolutionstothetransientquantumhydrodynamicequations
AT riald localexistenceofsolutionstothetransientquantumhydrodynamicequations
_version_ 1807319440646209536