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SUMMARY:Thomas Yizhao Hou (California Institute of Technology)
DTSTART:20200528T150000Z
DTEND:20200528T155000Z
DTSTAMP:20260423T021032Z
UID:IMS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IMS/21/">Rec
 ent Progress on Singularity Formation of 3D Euler Equations and Related Mo
 dels</a>\nby Thomas Yizhao Hou (California Institute of Technology) as par
 t of PDE seminar via Zoom\n\n\nAbstract\nWhether the 3D incompressible Eul
 er equations can develop a singularity in finite time from smooth initial 
 data is one of the most challenging problems in mathematical fluid dynamic
 s. We first review the numerical evidence of finite time singularity for 3
 D axisymmetric Euler equations by Luo and Hou. The singularity is a ring l
 ike singularity that occurs at a stagnation point in the symmetry plane lo
 cated at the boundary of the cylinder. We then present a novel method of a
 nalysis and prove that the 1D HL model develops finite time self-similar s
 ingularity. We also apply this method of analysis to prove finite time sel
 f-similar blowup of the original De Gregorio model for some smooth initial
  data on the real line with compact support.  Self-similar blowup results 
 for the generalized De Gregorio model for the entire range of parameter on
  the real line or on a circle have been obtained for Holder continuous ini
 tial data with compact support. Finally\, we report our recent progress in
  analyzing the finite time singularity of the axisymmetric 3D Euler equati
 ons with initial data considered by Luo and Hou.\n\nHere is the poster of 
 this talk: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%208th.p
 df?dl=0\nPlease visit our website to get more information: nguyenquochung1
 241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/21/
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