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Stable Self-similar Blowup in the Supercritical Heat Flow of Harmonic Maps by Biernat, Paweł; Donninger, Roland; Schörkhuber, Birgit is a scholarly article available to read on EtoBox.

What is Stable Self-similar Blowup in the Supercritical Heat Flow of Harmonic Maps about?

We consider the heat flow of corotational harmonic maps from $\mathbb R^3$ to the three-sphere and prove the nonlinear asymptotic stability of a particular self-similar shrinker that is not known in closed form. Our method provides a novel, systematic, robust, and constructive approach to the stability analysis of self-similar blowup in parabolic evolution equations. In particular, we completely avoid using delicate Lyapunov functionals, monotonicity formulas, indirect arguments, or fragile parabolic structure like the maximum principle. As a matter of fact, our approach reduces the nonlinear stability analysis of self-similar shrinkers to the spectral analysis of the associated self-adjoint linearized operators.

Author

Biernat, Paweł; Donninger, Roland; Schörkhuber, Birgit

Published

2016

Language

EN