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arXiv · 1904.11826

Scattering for the mass super-critical perturbations of the mass critical nonlinear Schr\"odinger equations

Xing Cheng
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Abstract

We consider the Cauchy problem for the nonlinear Schr\"odinger equation with double nonlinearities with opposite sign, with one term is mass-critical and the other term is mass-supercritical and energy-subcritical, which includes the famous two-dimensional cubic-quintic nonlinear Schr\"odinger equaton. We prove global wellposedness and scattering in $H^1(\mathbb{R}^d)$ below the threshold for non-radial data when $1 \le d \le 4$.

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Xing Cheng. 2019-04-25. Scattering for the mass super-critical perturbations of the mass critical nonlinear Schr\"odinger equations. https://arxiv.org/abs/1904.11826

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