Abstract

We consider the cubic-quintic nonlinear Schrödinger equation in two space dimensions. For this model, X. Cheng established scattering for $H^1$ data with mass strictly below that of the ground state for the cubic NLS. Subsequently, R. Carles and C. Sparber utilized the pseudoconformal energy estimate to obtain scattering at the sharp threshold for data belonging to a weighted Sobolev space. In this work, we remove the weighted assumption and establish scattering at the threshold for radial data in $H^1.$

中文翻译：

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二维径向三次五次 NLS 的阈值散射

摘要

我们在二维空间中考虑三次五次非线性薛定谔方程。对于这个模型，X. Cheng 建立了散射$H^1$质量严格低于立方 NLS 基态的数据。随后，R. Carles 和 C. Sparber 利用伪共形能量估计来获得属于加权 Sobolev 空间的数据在尖锐阈值处的散射。在这项工作中，我们去除了加权假设并在阈值处为径向数据建立散射$H^1.$