In this paper we study global existence of weak solutions for the quantum hydrodynamics system in two-dimensional energy space. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach replaces the WKB formalism with a polar decomposition theory which is not limited by the presence of vacuum regions. In this way we set up a self consistent theory, based only on particle density and current density, which does not need to define velocity fields in the nodal regions. The mathematical techniques we use in this paper are based on uniform (with respect to the approximating parameter) Strichartz estimates and the local smoothing property.

The Quantum Hydrodynamics System in Two Space Dimensions

Antonelli P;Marcati P
2012

Abstract

In this paper we study global existence of weak solutions for the quantum hydrodynamics system in two-dimensional energy space. We do not require any additional regularity and/or smallness assumptions on the initial data. Our approach replaces the WKB formalism with a polar decomposition theory which is not limited by the presence of vacuum regions. In this way we set up a self consistent theory, based only on particle density and current density, which does not need to define velocity fields in the nodal regions. The mathematical techniques we use in this paper are based on uniform (with respect to the approximating parameter) Strichartz estimates and the local smoothing property.
quantum hydrodynamics; weak solutions
File in questo prodotto:
File Dimensione Formato  
2012_ArchRationMechAnal_203_Antonelli.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 325.32 kB
Formato Adobe PDF
325.32 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12571/2139
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 60
  • ???jsp.display-item.citation.isi??? 59
social impact