Blowup of solutions for compressible viscoelastic fluid
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916935534379008 |
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| author | Boyaval, Sébastien Wang, Na Hu, Yuxi |
| author_facet | Boyaval, Sébastien Wang, Na Hu, Yuxi |
| contents | We prove finite-time blowup of classical solutions for the compressible Upper Convective Maxwell (UCM) viscoelastic fluid system. By establishing a key energy identity and adapting Sideris' method for compressible flows, we derive a Riccati-type inequality for a momentum functional. For initial data with compactly supported perturbations satisfying a sufficiently large condition, all classical solutions lose regularity in finite time. This constitutes the first rigorous blowup result for multidimensional compressible viscoelastic fluids. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_04924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blowup of solutions for compressible viscoelastic fluid Boyaval, Sébastien Wang, Na Hu, Yuxi Analysis of PDEs Classical Physics We prove finite-time blowup of classical solutions for the compressible Upper Convective Maxwell (UCM) viscoelastic fluid system. By establishing a key energy identity and adapting Sideris' method for compressible flows, we derive a Riccati-type inequality for a momentum functional. For initial data with compactly supported perturbations satisfying a sufficiently large condition, all classical solutions lose regularity in finite time. This constitutes the first rigorous blowup result for multidimensional compressible viscoelastic fluids. |
| title | Blowup of solutions for compressible viscoelastic fluid |
| topic | Analysis of PDEs Classical Physics |
| url | https://arxiv.org/abs/2509.04924 |