The Quantum Hydrodynamics System in Two Space Dimensions

Paolo Antonelli; Pierangelo Marcati

doi:10.1007/s00205-011-0454-7

The Quantum Hydrodynamics System in Two Space Dimensions

Paolo Antonelli, Pierangelo Marcati

Research output: Contribution to journal › Article › peer-review

80 Scopus citations

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.

Original language	English (US)
Pages (from-to)	499-527
Number of pages	29
Journal	Archive for Rational Mechanics and Analysis
Volume	203
Issue number	2
DOIs	https://doi.org/10.1007/s00205-011-0454-7
State	Published - Sep 16 2011
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: PAOLO ANTONELLI is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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AB - 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.

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The Quantum Hydrodynamics System in Two Space Dimensions

Abstract

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