SNSF Consolidator Grant awarded to Prof. Joachim Krieger
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Prof. Joachim Krieger has been awarded a CONSOLIDATOR GRANT by the SNSF in the context of the so-called “Temporary Backup Schemes” for the European Research Council (ERC) grants. This transitional measure of the SNSF offers the awardee an adequate substitute for ERC grants.
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WAVECONC - Concentration and dispersion phenomena for nonlinear waves
We investigate projects related to global existence and singularity formation for critical as well as supercritical nonlinear waves, arising as models in physics. First, we will develop optimal results on global existence, scattering and space-time bounds for the critical Wave Maps (arbitrary targets), Maxwell-Klein Gordon and Yang-Mills equations on Minkowski space.
Second, we will aim to exhibit multi-soliton type blow up solutions and study their stability for critical Wave Maps as well as the pure power critical nonlinear wave equation. For the latter, we aim at establishing the threshold conjecture, describing all solutions.
Third, we shall study certain large solutions for defocussing supercritical nonlinear wave equations. Finally, we also aim to study critical Wave Maps on curved geometries, with a view toward global existence for $U(1)$-symmetry reduced Einstein's equations, as well as the Vanishing Mean Curvature equation on Minkowski space which models evolution of strings.
Duration of the project: 60 months
Total Amount: CHF 1’367’235.-
Domains: Mathematics, Mathematical physics, analysis