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...
Autores principales: | , |
---|---|
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: |
id |
paper:paper_02182025_v12_n4_p485_Jungel |
---|---|
record_format |
dspace |
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 |
_version_ |
1768542360973606912 |