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SUMMARY:Bonn-Cologne Analysis & PDE Workshop SS 2026
DTSTART:20260605T121500Z
DTEND:20260605T160000Z
DTSTAMP:20260526T042400Z
UID:indico-event-1340@math-events.uni-bonn.de
CONTACT:shaoliu@math.uni-bonn.de
DESCRIPTION:Schedule\, Titles\, and Abstracts: \n14:15 - Jean-Marc Delort
  (Université de Paris XIII (Paris-Nord))  \nTitle: Blowing up solutions
  for one dimensional Klein-Gordon equations\nAbstract: Consider  a quasi-
 linear (or semi-linear) cubic Klein-Gordon equation in one space dimension
  with small\, smooth and decaying initial data. It is known that when the 
 nonlinearity satisfies a convenient ``null condition''\, the solution is g
 lobal. It is conjectured that\, if this null condition is not satisfied\, 
 generic initial data should give rise to solutions blowing up at a time of
  magnitude similar to $\\pm e^{S_*/\\epsilon^2}$\, where $S_*>0$ and $0<\\
 epsilon\\ll 1$ is the size of the initial data. \nWe consider in this tal
 k equation\n$(\\partial_t^2-\\partial_x^2 +1)u = (\\partial_t u)^3$\, \nw
 here the cubic semi-linear nonlinearity does not satisfy the null conditio
 n. We construct a blowing up solution at time $T_*(\\epsilon) = e^{S_*/\\e
 psilon^2}$\, which at time $T_0(\\epsilon) = \\epsilon^{-2}T_*(\\epsilon)^
 {1-b}$ ($b>0$ small)\, satisfies smallness and decay conditions\, compatib
 le with those allowing one to prove global existence for the similar probl
 em when the nonlinearity satisfies the null condition. Moreover\, we have 
 an asymptotic description of $u$ close to the unique blowing up point $(T_
 *(\\epsilon)\,0)$.  \n15:15 - Coffee Break \n16:00 - Robert Schippa (Un
 iversity of Bonn)\nTitle: Wave packet decompositions and sharp bilinear e
 stimates for rough Hamiltonian flows\nAbstract: We obtain sharp bilinear 
 estimates for solutions to dispersive equations with $C^{1\,1}$-coefficien
 ts. These extend the results of Wolff (2001) and Tao (2003) to the case of
  coefficients with minimal pointwise regularity. If time permits\, we poin
 t out the application to local smoothing estimates for rough wave equation
 s. Based on joint works with Daniel Tataru (UC Berkeley) and Jan Rozendaal
  (IMPAN). \n17:00 - Érik De Amorim (University of Cologne)\nTitle: Exac
 t general-relativistic solutions with finite self-energy for discrete poi
 nt charges under Bopp-Podolsky electromagnetism\nAbstract: We present ---
  in a self-contained and elementary way --- the existence of a family of s
 tatic\, spherically symmetric spacetimes that solve the Einstein equations
  of General Relativity coupled to the electric field of a point charge und
 er the generalized laws of electromagnetism of Bopp-Landé-Thomas-Podolsky
  (BLTP for short). This is mathematically interesting\, albeit not physica
 lly realistic\, because the point charge is not plagued by the problem of 
 the "infinite self-force" that occurs with the physical solution (the so-c
 alled Reissner-Nordström spacetime). This means that further rigorous stu
 dies of the motion of point charges in GR can in theory be carried out usi
 ng BLTP theory as a toy model. Time permitting\, we will also discuss the 
 difficulties that arise in the same type of study for two interacting part
 icles. All of the needed prerequisites from Physics\, like Electromagnetis
 m and Relativity\, and Math\, like hypergeometric functions and differenti
 al equations as perturbation problems\, will be covered during the talk. 
 \n18:30 - Dinner \n \n\nhttps://math-events.uni-bonn.de/event/1340/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1340/
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