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 conduct numerical simulations. The research group is supported by the University of Vienna and the FWF (Austrian Science Fund) via Projects P 34560 (PI Roland Donninger), P 34387 (PI Irfan Glogić), and P 36455 (PI Maciej Maliborski).
Current Members
- Roland Donninger (Head of Group)
- Irfan Glogić (Postdoc, supported by FWF)
- Maciej Maliborski (Postdoc, supported by FWF)
- David Wallauch (Postdoc, supported by FWF)
- Andras Bonk (PhD student, supported by FWF)
- Frederick Moscatelli (PhD student, supported by FWF)
- Matthias Ostermann (PhD student, supported by VSM)
Former members
- Ziping Rao (PhD student, graduated in 2019)
Recent Publications and Preprints
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Roland Donninger.
Spectral theory and self-similar blowup in wave equations.
Preprint arXiv:2310.12016.
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Irfan Glogić.
Global-in-space stability of singularity formation for Yang-Mills fields in higher dimensions.
Preprint arXiv:2305.10312.
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Matthias Ostermann.
Stable blowup for focusing semilinear wave equations in all dimensions.
Preprint arXiv:2304.08187.
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Irfan Glogić, Sarah Kistner, and Birgit Schörkhuber.
Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions.
Preprint arXiv:2304.04104.
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Roland Donninger and David Wallauch. Optimal blowup stability for three-dimensional wave maps. Preprint arXiv:2212.08374.
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Irfan Glogić and Birgit Schörkhuber.
Stable singularity formation for the Keller-Segel system in three dimensions.
Preprint arXiv:2209.11206.
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Matthias Ostermann.
A characterisation of the subspace of radially symmetric functions in Sobolev spaces.
Preprint arXiv:2209.02286.
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Po-Ning Chen, Roland Donninger, Irfan Glogić, Michael McNulty, Birgit Schörkhuber.
Co-dimension one stable blowup for the quadratic wave equation beyond the light cone.
Preprint arXiv:2209.07905.
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Irfan Glogić. Globally stable blowup profile for supercritical wave maps in all dimensions. Preprint arXiv:2207.06952.
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David Wallauch. Strichartz estimates and blowup stability for energy critical nonlinear wave equations.
Preprint arXiv:2204.03388.
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Roland Donninger and David Wallauch. Optimal blowup stability for supercritical wave maps. Preprint arXiv:2201.11419.
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Elek Csobo, Irfan Glogić, and Birgit Schörkhuber. On
blowup for the supercritical quadratic wave
equation. Preprint arXiv:2109.11931.
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Roland Donninger and Matthias Ostermann. A globally stable self-similar blowup profile in energy supercritical Yang-Mills theory. Preprint arXiv:2108.13668.
- Irfan Glogić. Stable blowup for the supercritical hyperbolic Yang-Mills equations. Preprint arXiv:2104.01839.
- Roland Donninger and David Wallauch. Blowup behavior of strongly perturbed wave equations. Preprint arXiv:2006.04600.
- Roland Donninger and Irfan Glogić.
Strichartz estimates for the one-dimensional wave equation.
Transactions of the American Mathematical Society 373(6):4051-4083, 2020.
- Irfan Glogić and Birgit Schörkhuber.
Nonlinear stability of homothetically shrinking Yang-Mills solitons
in the equivariant case.
Preprint arXiv:1910.03306.
- 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
113(1):55-94, 2019.
- Irfan Glogić, Maciej Maliborski, and Birgit Schörkhuber.
Threshold for blowup for the supercritical cubic wave equation.
Preprint arXiv:1905.13739.
- Roland Donninger and Athanasios Chatzikaleas. Stable blowup for the cubic wave equation in higher dimensions. Journal of Differential Equations
266(10):6809-6865, 2019.
- Roland Donninger and Ziping Rao. Blowup stability at optimal regularity for the critical wave equation.
Preprint arXiv:1811.08130.
- Irfan Glogić and Birgit Schörkhuber. Co-dimension one stable blowup for the supercritical cubic wave equation. Preprint arXiv:1810.07681.
Contact
University of Vienna
Faculty of Mathematics
Oskar-Morgenstern-Platz 1
1090 Vienna, Austria
Phone: +43 1 4277 55713
E-Mail: roland[dot]donninger[at]univie[dot]ac[dot]at