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SUMMARY:Collapse Versus Blow-Up and Global Existence in the Generalized Co
 nstantin–Lax–Majda Equation with and without dissipation - Pavel Lushn
 ikov (University of New Mexico)
DTSTART:20220909T080000Z
DTEND:20220909T090000Z
UID:TALK178160@talks.cam.ac.uk
DESCRIPTION:\n\n\nCo-authors: names and affiliations:\nDavid M. Ambrose (D
 rexel University)Michael Siegel (New Jersey Institute of Technology)Denis 
 A. Silantyev (University of Colorado\, Colorado Springs)\n\n\n\nWe &nbsp\;
 analyze the dynamics of singularities and finite time blowup ofgeneralized
  Constantin-Lax-Majda equation which corresponds tonon-potential effective
  motion of fluid with competing convection andvorticity stretching terms. 
 Both non-viscous fluid and fluid with varioustypes of dissipation includin
 g usual viscosity are considered. An infinitefamilies of exact solutions a
 re found together with the different types ofcomplex singularities approac
 hing the real line in finite times. Bothsolutions on the real line and per
 iodic solutions are considered. In theperiodic geometry\, a global-in-time
  existence of solutions &nbsp\;is proven whenthe data is small and dissipa
 tion is strong enough. The found analyticalsolutions on the real line allo
 w finite-time singularity formation forarbitrarily small data\, even for v
 arious form of dissipation\, therebyillustrating a critical difference bet
 ween the problems on the real lineand the circle. The analysis is compleme
 nted by accurate numericalsimulations\, which are able to track the format
 ion and motionsingularities in the complex plane. The computations validat
 e and extendthe analytical theory.\n&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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