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arXiv · 2406.16597

Self-similar blowup for the cubic Schr\"odinger equation

Roland Donninger·Birgit Schörkhuber
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Abstract

We give a rigorous proof for the existence of a finite-energy, self-similar solution to the focusing cubic Schr\"odinger equation in three spatial dimensions. The proof is computer-assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation. The latter is obtained by a standard pseudo-spectral method. The computer-assisted part of the rigorous proof uses nothing but fraction arithmetic in order to obtain quantitative bounds for the fixed point argument.

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Roland Donninger, Birgit Schörkhuber. 2024-06-24. Self-similar blowup for the cubic Schr\"odinger equation. https://arxiv.org/abs/2406.16597

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