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arXiv · 2212.08564

A new class of critical solutions for 1D cubic NLS

Anatole Guérin
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Abstract

The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity $F(L^\infty)$, and belonging to $\dot H^s$ for any $s <-1/2$. This problem is motivated by the lack of result for critical regularity initial condition. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals.

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Anatole Guérin. 2022-12-16. A new class of critical solutions for 1D cubic NLS. https://arxiv.org/abs/2212.08564

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