Iterative methods fail to solve NLS below the Sobolev embedding threshold on the Sierpinski gasket
Abstract
We show that the nonlinear Schrödinger equation on the Sierpinski gasket with a power nonlinearity of order $2k{+}1$ is \emph{not} locally well-posed for initial data just below the regularity threshold for the Sobolev embedding $H^s\subseteq L^\infty$. More precisely, the flow map fails to be $C^{2k+1}$-continuous in any Sobolev space $H^s$ below that threshold, and the threshold is independent of the power nonlinearity. This novel behavior significantly differs from other compact spaces such as the torus or the sphere, and it is directly connected to the existence of localized eigenfunctions.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematical Research Letters
- Publisher
- International Press of Boston
- Volume
- 33
- Issue
- 2
- Pages
- 639–666
- Publication date
- 1 January 2026
- Language
- EN