Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866929322039705600 |
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| author | Cheng, Xing Miao, Changxing Zhao, Lifeng |
| author_facet | Cheng, Xing Miao, Changxing Zhao, Lifeng |
| contents | We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in $H^1(\Bbb R^d)$ and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in $H^1(\Bbb R^d)$ below the threshold for radial data when $d\leq4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1401_2242 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case Cheng, Xing Miao, Changxing Zhao, Lifeng Analysis of PDEs 35L70, 35Q55 We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in $H^1(\Bbb R^d)$ and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in $H^1(\Bbb R^d)$ below the threshold for radial data when $d\leq4$. |
| title | Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case |
| topic | Analysis of PDEs 35L70, 35Q55 |
| url | https://arxiv.org/abs/1401.2242 |