29 citations · 57 across the 4 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…
Threshold for blowup for equivariant wave maps in higher dimensions
Paweł Biernat, Piotr Bizoń, Maciej Maliborski
We consider equivariant wave maps from to in supercritical dimensions . Using mixed numerical and analytic methods, we show that th…
Type II blow-up mechanism for supercritical harmonic map heat flow
Paweł Biernat, Yukihiro Seki
The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flo…