Blow-up solutions to a class of nonlinear coupled Schrödinger systems with power-type-growth nonlinearities
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910570394943488 |
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| author | Noguera, Norman |
| author_facet | Noguera, Norman |
| contents | In this work we consider a system of nonlinear Schrödinger equations whose nonlinearities satisfy a power-type-growth. First, we prove that the Cauchy problem is local and global well-posedness in $L^2$ and $H^1$. Next, we establish the existence of ground state solutions. Then we use these solutions to study the dichotomy of global existence versus blow-up in finite time. Similar results were presented in the reference Noguera N. and Pastor A. 2022 https://doi.org/10.1142/S0219199720500236 for the special case when the growth of the nonlinearities was quadratic. Here we will extend them to systems with nolinearities of order $p$ (cubic, quartic and so on). Finally, we recover some known results for two particular systems, one with quadratic and the other with cubic growth nolinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blow-up solutions to a class of nonlinear coupled Schrödinger systems with power-type-growth nonlinearities Noguera, Norman Analysis of PDEs 35A01, 35B44, 35J50, 35Q55 In this work we consider a system of nonlinear Schrödinger equations whose nonlinearities satisfy a power-type-growth. First, we prove that the Cauchy problem is local and global well-posedness in $L^2$ and $H^1$. Next, we establish the existence of ground state solutions. Then we use these solutions to study the dichotomy of global existence versus blow-up in finite time. Similar results were presented in the reference Noguera N. and Pastor A. 2022 https://doi.org/10.1142/S0219199720500236 for the special case when the growth of the nonlinearities was quadratic. Here we will extend them to systems with nolinearities of order $p$ (cubic, quartic and so on). Finally, we recover some known results for two particular systems, one with quadratic and the other with cubic growth nolinearities. |
| title | Blow-up solutions to a class of nonlinear coupled Schrödinger systems with power-type-growth nonlinearities |
| topic | Analysis of PDEs 35A01, 35B44, 35J50, 35Q55 |
| url | https://arxiv.org/abs/2408.09045 |