Type
ArticleKAUST Grant Number
KUK-I1-007-43Date
2011-09-16Online Publication Date
2011-09-16Print Publication Date
2012-02Permanent link to this record
http://hdl.handle.net/10754/599948
Metadata
Show full item recordAbstract
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 Natureae974a485f413a2113503eed53cd6c53
10.1007/s00205-011-0454-7