9 papers
Mode stability of self-similar wave maps without symmetry in higher dimensions
Roland Donninger, Frederick Moscatelli
We consider wave maps from -dimensional Minkowski space into the -sphere. For every , there exists an explicit self-similar solution that exhibits finite time b…
Future stability of large-data wave maps in energy-supercritical dimensions
Andras Bonk, Roland Donninger
We consider energy-supercritical co-rotational wave maps from Minkowski spacetime to the sphere in odd spatial dimensions. The equation admits an explicit co-rotational self-simila…
Blowup stability of wave maps without symmetry
Roland Donninger, Frederick Moscatelli
We study wave maps from -dimensional Minkowski space into the -sphere without any symmetry assumptions. There exists an explicit self-similar blowup solution and we prove…
Self-similar blowup for the cubic Schrödinger equation
Roland Donninger, Birgit Schörkhuber
We give a rigorous proof for the existence of a finite-energy, self-similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer-…
Self-similar blowup for mass supercritical Schrödinger equations
Roland Donninger, Lorenz Lichtnecker
We consider the focusing nonlinear Schrödinger equation in three spatial dimensions with powers close to three and prove the existence of a self-similar solution. This generalizes…
On stable self-similar blowup for corotational wave maps and equivariant Yang-Mills connections
Roland Donninger, Matthias Ostermann
We consider corotational wave maps from Minkowski spacetime into the sphere and the equivariant Yang-Mills equation for all energy-supercritical dimensions. Both models have explic…