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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08776 |
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| _version_ | 1866912703712329728 |
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| author | Georgiadis, Stefanos Spirito, Stefano |
| author_facet | Georgiadis, Stefanos Spirito, Stefano |
| contents | In this paper, we consider a family of one-dimensional fourth order evolution equations arising as gradient flows of the Korteweg energy, i.e. the $L^2$-norm of the first derivative of some power of the density. This family of equations generalizes the Quantum-Drift-Diffusion equation and the Thin-Film equation. We prove the global-in-time existence of {\em non-negative} weak solutions without requiring any upper bound on the exponent of the power of the density in the energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08776 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of non-negative weak solutions for $1D$ fourth order equations of gradient flow type Georgiadis, Stefanos Spirito, Stefano Analysis of PDEs Primary: 35G20, Secondary: 35K65, 35D30 In this paper, we consider a family of one-dimensional fourth order evolution equations arising as gradient flows of the Korteweg energy, i.e. the $L^2$-norm of the first derivative of some power of the density. This family of equations generalizes the Quantum-Drift-Diffusion equation and the Thin-Film equation. We prove the global-in-time existence of {\em non-negative} weak solutions without requiring any upper bound on the exponent of the power of the density in the energy. |
| title | On the existence of non-negative weak solutions for $1D$ fourth order equations of gradient flow type |
| topic | Analysis of PDEs Primary: 35G20, Secondary: 35K65, 35D30 |
| url | https://arxiv.org/abs/2511.08776 |