Mathematical Physics Seminar

October Schedule

No seminar on oct, 10,2007

Speaker: Michael Kiessling, Rutgers University
Date/Time/Place: Thursday, October 11, 2007 12:00pm Hill 705
Title: On The Relativistic Vlasov-Poisson System
Abstract: I survey recent joint work with A.Shadi Tahvildar-Zadeh, where the Cauchy problem has been revisited for the so-called relativistic Vlasov-Poisson system in the attractive case, originally studied by Glassey and Schaeffer in 1985. We have proved that a unique global classical solution exists whenever the positive, spherically symmetric initial datum f0 is compactly supported in momentum space, vanishes for vanishing test particle angular momentum, and its Lp norm is below a critical constant Cp >0 whenever p is not less than 3/2. We also showed that, if the bound Cp on the Lp norm of f0 is replaced by a bound C > Cp for any p in (1,oo),then classical initial data exist which lead to a blow-up in finite time. An upper bound on Cp is given for all p > 3/2, and the sharp value of Cp is computed explicitly for all p in (1,3/2]; in particular, Cp=0 for p in (1,3/2) but C3/2 >0. Thus, our L3/2 bound is optimal in the sense that it cannot be weakened to an Lp bound with p<3/2,whatever that bound. A new, non-gravitationalphysical vindication ofthe model which (unlike the gravitational one) is not restricted to weak fields, is also given.

No Seminar on oct, 18,2007 or oct,25,2007