Research Group Dispersive PDEs
The research group Dispersive PDEs at the Faculty of Mathematics of the University of Vienna is devoted to the rigorous analysis of dispersive partial differential equations such as nonlinear wave and Schrödinger equations, wave maps, Yang-Mills models, and related evolution equations arising in physics and/or geometry. We study these equations by developing new tools based on spectral theory, harmonic analysis, nonlinear functional analysis, and rigorous computer-assisted methods. In addition, in order to initiate rigorous studies, we occasionally conduct simple numerical simulations. The research group is supported by the University of Vienna and the FWF (Austrian Science Fund) via Project P30076.
- Ziping Rao (PhD student, graduated in 2019)
Recent Publications and Preprints
- Irfan Glogić and Birgit Schörkhuber.
Nonlinear stability of homothetically shrinking Yang-Mills solitons
in the equivariant case.
- David Borthwick, Roland Donninger, Enno Lenzmann, and Jeremy L. Marzuola. Existence and stability of Schrödinger solitons on noncompact manifolds.
SIAM Journal on Mathematical Analysis 51(5):3854-3901, 2019.
- Roland Donninger and Birgit Schörkhuber. Stable blowup for the
supercritical Yang-Mills heat flow.
Journal of Differential Geometry
- Roland Donninger and Irfan Glogić.
Strichartz estimates for the one-dimensional wave equation.
- Irfan Glogić, Maciej Maliborski, and Birgit Schörkhuber.
Threshold for blowup for the supercritical cubic wave equation.
- Roland Donninger and Athanasios Chatzikaleas. Stable blowup for the cubic wave equation in higher dimensions. Journal of Differential Equations
- Roland Donninger and Ziping Rao. Blowup stability at optimal regularity for the critical wave equation.
- Irfan Glogić and Birgit Schörkhuber. Co-dimension one stable blowup for the supercritical cubic wave equation. Preprint arXiv:1810.07681.
University of Vienna
Faculty of Mathematics
1090 Vienna, Austria
Phone: +43 1 4277 55713