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arXiv · 2211.07051

Sobolev norms of $L^2$-solutions to NLS

Roman V. Bessonov·Sergey A. Denisov
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Abstract

We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrodinger equation. For initial datum $q_0\in L^2(\mathbb{R})$ and $s\in [-1,0]$, we prove that there exists a conserved quantity that is equivalent to $H^s(\mathbb{R})$-norm of the solution.

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BibTeXRIS

Roman V. Bessonov, Sergey A. Denisov. 2022-11-14. Sobolev norms of $L^2$-solutions to NLS. https://doi.org/10.2140/pjm.2024.331.217

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