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SUMMARY:Theodore Drivas (Stony Brook University)
DTSTART:20211104T153000Z
DTEND:20211104T163000Z
DTSTAMP:20260423T022144Z
UID:SIAM-PDE/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/15/
 ">Compressible fluids\, entropy hierarchies\, and flocking</a>\nby Theodor
 e Drivas (Stony Brook University) as part of Seminar In the Analysis and M
 ethods of PDE (SIAM PDE)\n\n\nAbstract\nWe will discuss two types of one-d
 imensional compressible fluid equations\; Navier-Stokes models with local 
 dissipation in which the viscosity depends degenerately on the density and
  nonlocal models for collective dynamics which exhibit flocking behavior. 
 For the local models\, we prove large data global regularity for a class o
 f equations covering viscous shallow water. Another result proves a conjec
 ture of Peter Constantin on singularity formation for a model describing s
 lender axisymmetric fluid jets.  For the non-local models\, we establish a
  continuation criterion which says that smooth solutions exist so long as 
 no vacuum states form.  The method of proof involves introducing a hierarc
 hy of entropies to control the solution in terms of the minimum density.  
 We also show that any weak solutions which obeying an entropy inequality e
 xhibit flocking.  This reports on joint work with P. Constantin\, H. Nguye
 n\, F. Pasqualotto and R. Shvydkoy.\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/15/
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