TY - JOUR
T1 - The Quantum Hydrodynamics System in Two Space Dimensions
AU - Antonelli, Paolo
AU - Marcati, Pierangelo
N1 - 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.
PY - 2011/9/16
Y1 - 2011/9/16
N2 - 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.
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.
UR - http://hdl.handle.net/10754/599948
UR - http://link.springer.com/10.1007/s00205-011-0454-7
UR - http://www.scopus.com/inward/record.url?scp=84856482347&partnerID=8YFLogxK
U2 - 10.1007/s00205-011-0454-7
DO - 10.1007/s00205-011-0454-7
M3 - Article
SN - 0003-9527
VL - 203
SP - 499
EP - 527
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -