Sofja Kovalevskaja Research Group

The Sofja Kovalevskaja research group "Dispersive Wave Equations: Blowup and Asymptotics" was established in October 2014. The group is led by Roland Donninger and funded by the Humboldt Foundation via a Sofja Kovalevskaja Award. The total funding amounts to 1.5 million Euros for a period of five years. The group is hosted by Herbert Koch. We are also associated to the research group Analysis and Partial Differential Equations led by Herbert Koch and Christoph Thiele.

The main goal of the research group is to advance the theoretical understanding of nonlinear wave equations and related time evolution PDEs originating in mathematical physics, general relativity, and geometry. We also work in closely related areas such as spectral theory, harmonic analysis, functional analysis, and numerical simulations.

Group members

International collaborations

Activities

Workshop Singularity formation and long-time behavior in dispersive PDEs, March 14 - 18, 2016

Recent publications and preprints

  • Athanasios Chatzikaleas, Roland Donninger, and Irfan Glogić. On blowup of co-rotational wave maps in odd space dimensions. Preprint arXiv:1701.05082.
  • Ovidiu Costin, Roland Donninger, and Xiaoyue Xia. A proof for the mode stability of a self-similar wave map. Nonlinearity, 29(8):2451-2473, 2016.
  • Paweł Biernat, Roland Donninger, and Birgit Schörkhuber. Stable self-similar blowup in the supercritical heat flow of harmonic maps. Preprint arXiv:1610.09497.
  • Paweł Biernat and Roland Donninger. Construction of a spectrally stable self-similar blowup solution to the supercritical harmonic map heat flow. Preprint arXiv:1610.09496.
  • Paweł Biernat, Piotr Bizoń, and Maciej Maliborski. Threshold for blowup for equivariant wave maps in higher dimensions. Preprint arXiv:1608.07707.
  • Roland Donninger and Birgit Schörkhuber. On blowup in supercritical wave equations. Communications in Mathematical Physics, 346(3):907–943, 2016.
  • Roland Donninger and Birgit Schörkhuber. Stable blowup for the supercritical Yang-Mills heat flow. Preprint arXiv:1604.00303.
  • Ovidiu Costin, Roland Donninger, and Irfan Glogić. Mode stability of self-similar wave maps in higher dimensions. Preprint arXiv:1604.00303.
  • Ovidiu Costin, Roland Donninger, Irfan Glogić, and Min Huang. On the stability of self-similar solutions to nonlinear wave equations. Communications in Mathematical Physics, 343(1):299–310, 2016.
  • Matthew Creek, Roland Donninger, Wilhelm Schlag, and Stanley Snelson. Linear stability of the Skyrmion. Preprint arXiv:1603.03662.
  • Paweł Biernat and Yukihiro Seki. Type II blow-up mechanism for supercritical harmonic map heat flow. Preprint arXiv:1601.01831.
  • Annegret Y. Burtscher and Roland Donninger. Hyperboloidal evolution and global dynamics for the focusing cubic wave equation. Preprint arXiv:1511.08600.
  • Roland Donninger. Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation. Preprint arXiv:1509.02041.
  • Paweł Biernat and Piotr Bizoń. Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions. Communications in Mathematical Physics, 338(3):1443-1450, 2015.
  • Annegret Y. Burtscher. Length structures on manifolds with continuous Riemannian metrics. New York Journal of Mathematics, 21:273-296, 2015.
  • Roland Donninger and Birgit Schörkhuber. Stable blowup for wave equations in odd space dimensions. Preprint arXiv:1504.00808.
  • Roland Donninger and Birgit Schörkhuber. A spectral mapping theorem for perturbed Ornstein-Uhlenbeck operators on L^2(R^d). Journal of Functional Analysis, 268(9):2479-2524, 2015.