University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Friday 3 November, 12:10-1:00pm
                          6183 Bahen Center      



SPEAKER:  Pierre Raphael

TITLE:    Stable self similar blow up dynamics for some gravitational
	  Vlasov-Poisson systems


ABSTRACT: The gravitational Vlasov Poisson system f_t+v.\nabla_x 
	  f-E.\nabla_v f=0, (x,v)\in R^3, f(t,x,v)\geq 0, where E is 
	  the Poisson field associated to the density \rho(t,x)=\int 
	  f(t,x,v)dv, describes the mechanical state of a stellar system 
	  subject to its own gravity. From the mathematical point of 
	  view, this a focusing nonlinear transport equation. From a 
	  result of Pfaffelmoser (92), see also Lions-Perthame (91), 
	  given a smooth compactly supported initial data, there exists 
	  a unique global solution. There exists a hierarchy of models 
	  to take into account further relativistic effects, the 
	  simplest one being the so called relativistic gravitational 3d 
	  (VP) system: f_t+\frac{v}{\sqrt{1+|v|^2}}.\nabla_x f
	  -E.\nabla_v f=0 with the same nonlinearity E. A striking 
	  feature as proved by Glassey, Schaeffer(85), from a viriel 
	  type argument is that this equation now admits finite time blow 
	  up solutions. Note nevertheless that like for other nonlinear 
	  dispersive PDE's, the argument is purely obstructive and gives 
	  no information on the singularity formation. We prove the
	  existence and the stability of a self-similar blow up for this 
	  system. This is joint work with Florian Mehats and Mohammed 
	  Lemou.


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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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