| Abstract: |
| In this talk, I will show the scattering of the quintic defocusing nonlinear Schr\"odinger equations on cylinders $R \times T$. By establishing an abstract linear profile decomposition, we can then reduce the scattering to the scattering of an quintic resonant Schr\"odinger system. By using the argument developed by B. Dodson in the mass-critical nonlinear Schr\"odinger equation, we can prove the scattering of the Schr\"odinger system. Meantime, we also deal with scattering of the quintic nonlinear Schr\"odinger equations with partial harmonic potentials by using the arguments developed in the scattering of the nonlinear Schr\"odinger equations on cylinders. |
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