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    The Quantum Hydrodynamics System in Two Space Dimensions

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    Type
    Article
    Authors
    Antonelli, Paolo
    Marcati, Pierangelo
    KAUST Grant Number
    KUK-I1-007-43
    Date
    2011-09-16
    Online Publication Date
    2011-09-16
    Print Publication Date
    2012-02
    Permanent link to this record
    http://hdl.handle.net/10754/599948
    
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    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.
    Sponsors
    PAOLO ANTONELLI is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Archive for Rational Mechanics and Analysis
    DOI
    10.1007/s00205-011-0454-7
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00205-011-0454-7
    Scopus Count
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    Publications Acknowledging KAUST Support

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