Handle URI:
http://hdl.handle.net/10754/599948
Title:
The Quantum Hydrodynamics System in Two Space Dimensions
Authors:
Antonelli, Paolo; Marcati, Pierangelo
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. © 2011 Springer-Verlag.
Citation:
Antonelli P, Marcati P (2011) The Quantum Hydrodynamics System in Two Space Dimensions. Archive for Rational Mechanics and Analysis 203: 499–527. Available: http://dx.doi.org/10.1007/s00205-011-0454-7.
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
16-Sep-2011
DOI:
10.1007/s00205-011-0454-7
Type:
Article
ISSN:
0003-9527; 1432-0673
Sponsors:
PAOLO ANTONELLI is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonelli, Paoloen
dc.contributor.authorMarcati, Pierangeloen
dc.date.accessioned2016-02-28T06:33:03Zen
dc.date.available2016-02-28T06:33:03Zen
dc.date.issued2011-09-16en
dc.identifier.citationAntonelli P, Marcati P (2011) The Quantum Hydrodynamics System in Two Space Dimensions. Archive for Rational Mechanics and Analysis 203: 499–527. Available: http://dx.doi.org/10.1007/s00205-011-0454-7.en
dc.identifier.issn0003-9527en
dc.identifier.issn1432-0673en
dc.identifier.doi10.1007/s00205-011-0454-7en
dc.identifier.urihttp://hdl.handle.net/10754/599948en
dc.description.abstractIn 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. © 2011 Springer-Verlag.en
dc.description.sponsorshipPAOLO ANTONELLI is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.titleThe Quantum Hydrodynamics System in Two Space Dimensionsen
dc.typeArticleen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionUniversita degli Studi dell'Aquila, L'Aquila, Italyen
kaust.grant.numberKUK-I1-007-43en
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