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BEGIN:VEVENT
UID:13e9306f20bb3c17242f6d8b9224af76
CATEGORIES:Nonlinear Analysis
CREATED:20210427T114234
SUMMARY:The Interplay between Analysis and Computation in Studying 3D Euler Singularity
LOCATION:Zoom
DESCRIPTION:Abstract: Whether the 3D incompressible Euler equations can develop a singu
 larity in finite time from smooth initial data is one of the most challengi
 ng problems in mathematical fluid dynamics. We first review the numerical e
 vidence of finite time singularity for 3D axisymmetric Euler equations by L
 uo and Hou. The singularity is a ring like singularity that occurs at a sta
 gnation point in the symmetry plane located at the boundary of the cylinder
 . We then present a novel method of analysis and prove that the 1D HL model
  and the original De Gregorio model develop finite time self-similar singul
 arity. This analysis has been generalized to prove finite time singularity 
 of the 2D Boussinesq and 3D Euler equations with C^{1,alpha} initial veloci
 ty and boundary, whose solutions share some essential features similar to t
 hose reported in the Luo-Hou computation. Finally, we present some recent n
 umerical results on singularity formation of the 3D axisymmetric Navier-Sto
 kes equations with degenerate diffusion coefficients.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract:&nbsp;</strong>Whether the 3D incompressible Euler equa
 tions can develop a singularity in finite time from smooth initial data is 
 one of the most challenging problems in mathematical fluid dynamics. We fir
 st review the numerical evidence of finite time singularity for 3D axisymme
 tric Euler equations by Luo and Hou. The singularity is a ring like singula
 rity that occurs at a stagnation point in the symmetry plane located at the
  boundary of the cylinder. We then present a novel method of analysis and p
 rove that the 1D HL model and the original De Gregorio model develop finite
  time self-similar singularity. This analysis has been generalized to prove
  finite time singularity of the 2D Boussinesq and 3D Euler equations with C
 ^{1,alpha} initial velocity and boundary, whose solutions share some essent
 ial features similar to those reported in the Luo-Hou computation. Finally,
  we present some recent numerical results on singularity formation of the 3
 D axisymmetric Navier-Stokes equations with degenerate diffusion coefficien
 ts.</p>
CONTACT:Thomas Yizhao Hou, California Institute of Technology
X-EXTRAINFO:https://rutgers.zoom.us/j/92489375526?pwd=K0xyMEpHQXIrc0NLMEtqUWdSNHF4QT09#
 success\nMeeting ID: 924 8937 5526 Passcode: 565238
DTSTAMP:20260828T185709
DTSTART;TZID=America/New_York:20210427T134000
DTEND;TZID=America/New_York:20210427T144000
SEQUENCE:0
TRANSP:OPAQUE
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