Quantum fluids and related problems

Wednesday, July 22, 2009 - 2:00pm - 2:50pm
EE/CS 3-180
Pierangelo Marcati (Università di L'Aquila)
It will be reviewed briefly various physical models leading to a
description based on Quantum Hydrodynamics: Superfluidity, BEC,
superconductivity, semiconductors and there will be recalled various
derivations of the PDE system.
The main result (joint with P. Antonelli) shows the global existence
of irrotational weak solutions with
the sole assumption of finite energy, without any smallness or any
further smoothness of the initial data.
The approach is based on various tools, namely the wave functions
polar decomposition, the construction of approximate solution via a
fractional steps method which iterates a Schrödinger Madelung picture
with a suitable wave function updating mechanism.
Therefore several a priori bounds of energy, dispersive and local
smoothing type, allow to prove the compactness of the approximating
sequences. A different approach can be used to study small
disturbances of subsonic (in the QHD sense) steady states.
Some improvements may are shown to be possible in the 2-D analysis.
MSC Code: