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UID:news1100@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20201102T110041
DTSTART;TZID=Europe/Zurich:20201111T141500
SUMMARY:Seminar Analysis and Mathematical Physics: Lars Eric Hientzsch (Ins
 titut Fourier\, University of Grenoble Alpes)
DESCRIPTION:The quantum Navier-Stokes (QNS) equations describe a compressib
 le fluid including a degenerate density dependent viscosity and a dispersi
 ve tensor accounting for capillarity effects. The system can be seen as vi
 scous correction of the Quantum Hydrodynamics (QHD) arising e.g. as protot
 ype model in the description of superfluidity. We consider the (QNS) syste
 m on the whole space with non-trivial farfield behaviour providing the sui
 table framework to study coherent structures and the incompressible limit.
 \\r\\nFirst\, we prove global existence of finite energy weak solutions (F
 EWS) in dimension two and three. To compensate for the lack of control of 
 the velocity field around vacuum regions\, we construct approximate soluti
 ons to a truncated formulation of (QNS) on a sequence of invading domains.
  Suitable compactness properties are inferred from the Bresch-Desjadins en
 tropy estimates. This is joint work with P. Antonelli and S. Spirito.\\r\\
 nSecond\, we address the low Mach number limit for FEWS to the (QNS) syste
 m (in collaboration with P. Antonelli and P. Marcati). The main novelty is
  a precise analysis of the acoustic dispersion altered by the presence of 
 the dispersive capillarity tensor. The linearised system is governed by 
 the Bogoliubov dispersion relation. The desired decay of the acoustic part
  follows from refined Strichartz estimates. 
X-ALT-DESC:<p>The quantum Navier-Stokes (QNS) equations describe a compress
 ible fluid including a degenerate density dependent viscosity and a disper
 sive tensor accounting for capillarity effects. The system can be seen as 
 viscous correction of the Quantum Hydrodynamics (QHD) arising e.g. as prot
 otype model in the description of superfluidity. We consider the (QNS) sys
 tem on the whole space with non-trivial farfield behaviour providing the s
 uitable framework to study coherent structures and the incompressible limi
 t.</p>\n<p>First\, we prove global existence of finite energy weak solutio
 ns (FEWS) in dimension two and three. To compensate for the lack of contro
 l of the velocity field around vacuum regions\, we construct approximate s
 olutions to a truncated formulation of (QNS) on a sequence of invading dom
 ains. Suitable compactness properties are inferred from the Bresch-Desjadi
 ns entropy estimates. This is joint work with P. Antonelli and S. Spirito.
 </p>\n<p>Second\, we address the low Mach number limit for FEWS to the (QN
 S) system (in collaboration with P. Antonelli and P. Marcati). The main no
 velty is a precise analysis of the acoustic dispersion altered by the pres
 ence of the dispersive capillarity tensor. The&nbsp\;linearised&nbsp\;syst
 em is governed by the Bogoliubov dispersion relation. The desired decay of
  the acoustic part follows from refined Strichartz estimates.&nbsp\;</p>
DTEND;TZID=Europe/Zurich:20201111T160000
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