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...

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Detalles Bibliográficos
Autores principales: Mariani, María Cristina, Rial, Diego Fernando
Publicado: 2002
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p485_Jungel
http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p485_Jungel
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_02182025_v12_n4_p485_Jungel2023-06-08T15:21:22Z Local existence of solutions to the transient quantum hydrodynamic equations Mariani, María Cristina Rial, Diego Fernando 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. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p485_Jungel 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.
author Mariani, María Cristina
Rial, Diego Fernando
spellingShingle Mariani, María Cristina
Rial, Diego Fernando
Local existence of solutions to the transient quantum hydrodynamic equations
author_facet Mariani, María Cristina
Rial, Diego Fernando
author_sort Mariani, María Cristina
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
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p485_Jungel
http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p485_Jungel
work_keys_str_mv AT marianimariacristina localexistenceofsolutionstothetransientquantumhydrodynamicequations
AT rialdiegofernando localexistenceofsolutionstothetransientquantumhydrodynamicequations
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