Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914082755444736 |
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| author | Casteras, Jean-Baptiste Holopainen, Ilkka Monsaingeon, Léonard |
| author_facet | Casteras, Jean-Baptiste Holopainen, Ilkka Monsaingeon, Léonard |
| contents | We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension $N\geq 13$. Our solution is radially symmetric and converges asymptotically to the sum of two bubbles. The scale of one of the bubble is of order $1$ whereas the other one is of order $|t|^{-\frac{2}{N-12}}$. Moreover, the phase between the two bubbles form a right angle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14744 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation Casteras, Jean-Baptiste Holopainen, Ilkka Monsaingeon, Léonard Analysis of PDEs 35Q55, 35J30, 35B40 We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension $N\geq 13$. Our solution is radially symmetric and converges asymptotically to the sum of two bubbles. The scale of one of the bubble is of order $1$ whereas the other one is of order $|t|^{-\frac{2}{N-12}}$. Moreover, the phase between the two bubbles form a right angle. |
| title | Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation |
| topic | Analysis of PDEs 35Q55, 35J30, 35B40 |
| url | https://arxiv.org/abs/2304.14744 |