KAUST Grant NumberKUK-I1-007-43
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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.
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.
SponsorsPAOLO ANTONELLI is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST).