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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| Format: | Article |
| Language: | English |
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AIMS Press
2024-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241460?viewType=HTML |
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| author | Saleh Almuthaybiri Radhia Ghanmi Tarek Saanouni |
| author_facet | Saleh Almuthaybiri Radhia Ghanmi Tarek Saanouni |
| author_sort | Saleh Almuthaybiri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-39acfff09db14540a4731e1d43d72d39 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-39acfff09db14540a4731e1d43d72d392025-08-20T02:18:43ZengAIMS PressAIMS Mathematics2473-69882024-10-01911302303026210.3934/math.20241460On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowupSaleh Almuthaybiri0Radhia Ghanmi 1Tarek Saanouni21. Department of Mathematics, College of Science, Qassim University, Saudi Arabia2. University of Tunis El Manar, Faculty of Sciences of Tunis, 2092 Tunis, LR03ES04 Partial Differential Equations, Tunisia1. Department of Mathematics, College of Science, Qassim University, Saudi ArabiaThis 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.https://www.aimspress.com/article/doi/10.3934/math.20241460?viewType=HTMLschrödinger problemenergy-criticalnonlinear equationsfixed point methodglobal existencescatteringblowup |
| spellingShingle | Saleh Almuthaybiri Radhia Ghanmi Tarek Saanouni On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup AIMS Mathematics schrödinger problem energy-critical nonlinear equations fixed point method global existence scattering blowup |
| title | On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup |
| title_full | On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup |
| title_fullStr | On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup |
| title_full_unstemmed | On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup |
| title_short | On the nonlinear Schrödinger equation with critical source term: global well-posedness, scattering and finite time blowup |
| title_sort | on the nonlinear schrodinger equation with critical source term global well posedness scattering and finite time blowup |
| topic | schrödinger problem energy-critical nonlinear equations fixed point method global existence scattering blowup |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241460?viewType=HTML |
| work_keys_str_mv | AT salehalmuthaybiri onthenonlinearschrodingerequationwithcriticalsourcetermglobalwellposednessscatteringandfinitetimeblowup AT radhiaghanmi onthenonlinearschrodingerequationwithcriticalsourcetermglobalwellposednessscatteringandfinitetimeblowup AT tareksaanouni onthenonlinearschrodingerequationwithcriticalsourcetermglobalwellposednessscatteringandfinitetimeblowup |