On the well-possedness of time-dependent three-dimensional Euler fluid flows
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913471182929920 |
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| author | Bulíček, Miroslav Málek, Josef |
| author_facet | Bulíček, Miroslav Málek, Josef |
| contents | We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large, critical value. Once the velocity gradient exceeds this threshold, a dissipation mechanism is activated. Assuming that the fluid, after such an activation, dissipates the energy in a specific manner, we prove that the corresponding initial-boundary-value problem is globally-in-time well-posed in the sense of Hadamard. In particular, we show that for an arbitrary, sufficiently regular, initial velocity there is a unique weak solution to the spatially periodic problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the well-possedness of time-dependent three-dimensional Euler fluid flows Bulíček, Miroslav Málek, Josef Analysis of PDEs 35K59, 35K92, 35D30, 76D03 We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large, critical value. Once the velocity gradient exceeds this threshold, a dissipation mechanism is activated. Assuming that the fluid, after such an activation, dissipates the energy in a specific manner, we prove that the corresponding initial-boundary-value problem is globally-in-time well-posed in the sense of Hadamard. In particular, we show that for an arbitrary, sufficiently regular, initial velocity there is a unique weak solution to the spatially periodic problem. |
| title | On the well-possedness of time-dependent three-dimensional Euler fluid flows |
| topic | Analysis of PDEs 35K59, 35K92, 35D30, 76D03 |
| url | https://arxiv.org/abs/2408.09573 |