93 citations · 337 across the 42 of their papers we have counts for
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Stable self-similar blowup in the supercritical heat flow of harmonic maps
Paweł Biernat, Roland Donninger, Birgit Schörkhuber
We consider the heat flow of corotational harmonic maps from to the three-sphere and prove the nonlinear asymptotic stability of a particular self-similar shrinker th…
Construction of a spectrally stable self-similar blowup solution to the supercritical corotational harmonic map heat flow
Paweł Biernat, Roland Donninger
We prove the existence of a (spectrally) stable self-similar blow-up solution to the heat flow for corotational harmonic maps from to the three-sphere. In parti…
Stable blowup for the supercritical Yang-Mills heat flow
Roland Donninger, Birgit Schörkhuber
In this paper, we consider the heat flow for Yang-Mills connections on . In the equivariant setting, the Yang-Mills heat equation reduces to a si…
Mode stability of self-similar wave maps in higher dimensions
Ovidiu Costin, Roland Donninger, Irfan Glogić
We consider co-rotational wave maps from Minkowski space in dimensions to the -sphere. Recently, Bizoń and Biernat found explicit self-similar solutions for each dimension…
Linear stability of the Skyrmion
Matthew Creek, Roland Donninger, Wilhelm Schlag +1
We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.