Blow-up results for Inhomogeneous fourth-order nonlinear Schrödinger Equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909678891433984 |
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| author | Scarpelli, Renzo Hespanha, Maicon |
| author_facet | Scarpelli, Renzo Hespanha, Maicon |
| contents | In this paper, we investigate the blow-up phenomenon of the $H^2$ norm of solutions to the inhomogeneous biharmonic Schrodinger equation in two distinct scenarios. First, we consider the case of negative energy, analyzing separately the cases of radial and non-radial solutions. Then, we examine the positive energy case, where the energy is below that of the ground state and the ``kinetic'' energy exceeds the corresponding value for the ground state, again distinguishing between radial and non-radial solutions. Our approach is based on convexity methods, employing virial identities in the analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_05518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up results for Inhomogeneous fourth-order nonlinear Schrödinger Equation Scarpelli, Renzo Hespanha, Maicon Analysis of PDEs 35Q55, 35Q44, 35B44 In this paper, we investigate the blow-up phenomenon of the $H^2$ norm of solutions to the inhomogeneous biharmonic Schrodinger equation in two distinct scenarios. First, we consider the case of negative energy, analyzing separately the cases of radial and non-radial solutions. Then, we examine the positive energy case, where the energy is below that of the ground state and the ``kinetic'' energy exceeds the corresponding value for the ground state, again distinguishing between radial and non-radial solutions. Our approach is based on convexity methods, employing virial identities in the analysis. |
| title | Blow-up results for Inhomogeneous fourth-order nonlinear Schrödinger Equation |
| topic | Analysis of PDEs 35Q55, 35Q44, 35B44 |
| url | https://arxiv.org/abs/2507.05518 |