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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/2506.23910 |
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| _version_ | 1866918318353416192 |
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| author | Schiffer, Stefan Xylander, Espen |
| author_facet | Schiffer, Stefan Xylander, Espen |
| contents | We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in anisotropic spaces. The abstract theory is then applied to formulate a variational solution concept for the non-Newtonian Navier--Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A variational view on constitutive laws in parabolic problems Schiffer, Stefan Xylander, Espen Analysis of PDEs 35Q30, 49J45, 76D05 We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in anisotropic spaces. The abstract theory is then applied to formulate a variational solution concept for the non-Newtonian Navier--Stokes equations. |
| title | A variational view on constitutive laws in parabolic problems |
| topic | Analysis of PDEs 35Q30, 49J45, 76D05 |
| url | https://arxiv.org/abs/2506.23910 |