On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup
This study explored the time asymptotic behavior of the Schrödinger equation with an inhomogeneous energy-critical nonlinearity. The approach follows the concentration-compactness method due to Kenig and Merle. To address the primary challenge posed by the singular inhomogeneous term, we utilized Ca...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-10-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241460?viewType=HTML |
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| Summary: | This study explored the time asymptotic behavior of the Schrödinger equation with an inhomogeneous energy-critical nonlinearity. The approach follows the concentration-compactness method due to Kenig and Merle. To address the primary challenge posed by the singular inhomogeneous term, we utilized Caffarelli-Kohn-Nirenberg weighted inequalities. This work notably expanded the existing literature by applying these techniques to higher spatial dimensions without requiring any spherically symmetric assumption. |
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| ISSN: | 2473-6988 |