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SUMMARY:The Cauchy problem for a fourth order version of the wave map equa
 tion. - Tobias Schmid\, Karlsruhe Institute of Technology
DTSTART:20180124T160000Z
DTEND:20180124T170000Z
UID:TALK100018@talks.cam.ac.uk
CONTACT:Ollie McEnteggart
DESCRIPTION:Harmonic maps are smooth maps (between manifolds) with vanishi
 ng tension field. In case the domain is endowed with a Lorentzian metric t
 his leads to a semilinear wave equation\, the so called wave map equation.
  We consider a fourth order version of the wave map equation and talk abou
 t aspects of the Cauchy problem\, including existence of local solutions f
 ollowing from energy estimates with a fourth order viscosity method\, glob
 al extension of the solutions in energy subcritical dimension d < 4 and co
 nstruction of solutions in low regularity.\nAfterwards we highlight some d
 ifferences in the techniques that apply to other geometric equations such 
 as the wave map equation and the Schrödinger map flow.
LOCATION:MR14\, Centre for Mathematical Sciences
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