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European Mathematical Society Publishing House
2016-09-19 17:05:18
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
4
2007
4
Nonlinear Waves and Dispersive Equations
Carlos
Kenig
University of Chicago, CHICAGO, UNITED STATES
Herbert
Koch
Universität Bonn, BONN, GERMANY
Daniel
Tataru
University of California, BERKELEY, UNITED STATES
Dispersive equations occur as asymptotic models for the propagation of linear and nonlinear waves. Mathematically they display an interplay between linear dispersion and nonlinear focusing and defocusing effects. They are linked to diverse areas of mathematics and physics, ranging from nonlinear optics over oscillatory integrals to integrable systems. The workshop focused on a PDE based approach to dispersive equations. Current activities covered by the workshop include: \begin{enumerate} \item Progress in understanding critical nonlinear Schr\"oder equations. Generalized Morawetz estimates and an induction on energy improved our understanding on the interaction of waves for nonlinear Schr\"odinger equations, which led to a treatment of many such critical equations. \item The study of dispersive equations with variable coefficients. During the last few years our understanding of wave propagation in nonhomogeneous situations improved considerably and there are now several interesting results on general relativity linearized at the Schwarzschild metric. This may be seen as a step towards nonlinear stability of the Schwarzschild metric. \item The large time asymptotics of solutions, including asymptotics of multisoliton solutions in the nonintegrable case and sharp asymptotics of singular solutions. \end{enumerate} There is a large number of promising young mathematicians working in this area. The meeting was attented by 45 participants. The organizers gave a strong preference to talks by young researchers.
Partial differential equations
General
2609
2670
10.4171/OWR/2007/44
http://www.ems-ph.org/doi/10.4171/OWR/2007/44