29 citations · 57 across the 4 of their papers we have counts for
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Hyperboloidal similarity coordinates and a globally stable blowup profile for supercritical wave maps
Paweł Biernat, Roland Donninger, Birgit Schörkhuber
We consider co-rotational wave maps from (1+3)-dimensional Minkowski space into the three-sphere. This model exhibits an explicit blowup solution and we prove the asymptotic nonlin…
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…
Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions
Paweł Biernat
We analyze the finite-time blow-up of solutions of the heat flow for -corotational maps . For each dimension we construct a countable fa…
Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres
Paweł Biernat, Piotr Bizoń
Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the -dimensional sphere to itse…