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SUMMARY:On the finite energy weak solutions to a system in Quantum Fluid D
 ynamics - Paolo Antonelli (Applied PDE group\, DAMTP)
DTSTART:20081031T140000Z
DTEND:20081031T150000Z
UID:TALK14789@talks.cam.ac.uk
CONTACT:4520
DESCRIPTION:In this talk we consider the global existence of weak solution
 s to the\nQuantum Hydrodynamics System (QHD) with initial data in the ener
 gy space\,\nwithout any smallness conditions. These types of models\, init
 ially proposed\nby Madelung\, have been extensively used in Physics to inv
 estigate\nsuperfluidity phenomena and\, more recently\, in the modeling of
  semiconductor\ndevices. Our approach is based on the formal equivalence b
 etween the QHD\nsystem and a nonlinear Schroedinger equation\, and on the 
 fractional step\nmethod to construct a sequence of approximate solutions. 
 A key ingredient\nwill be a wave function polar decomposition in order to 
 develop a suitable\nupdating mechanism and to give the quadratic terms in 
 the system a stable\nstructure depending on the wave function. Therefore s
 everal a priori bounds\nof energy\, dispersive and local smoothing type al
 low us to prove the\ncompactness of the approximate sequences. No uniquene
 ss result is provided.\n
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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