Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916086969008128 |
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| author | Burtea, Cosmin Szlenk, Maja |
| author_facet | Burtea, Cosmin Szlenk, Maja |
| contents | We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$ and the pressure is given by $\varrho^γ$, we construct a solution provided that $r>\frac{3d}{d+2}$ and $γ$ is sufficiently large, depending on the values of $r$. Additionally, we also show the existence for time-discretized model for Herschel-Bulkley fluids, where the viscosity has a singular part. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids Burtea, Cosmin Szlenk, Maja Analysis of PDEs 35Q35, 76N10, 35D30 We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$ and the pressure is given by $\varrho^γ$, we construct a solution provided that $r>\frac{3d}{d+2}$ and $γ$ is sufficiently large, depending on the values of $r$. Additionally, we also show the existence for time-discretized model for Herschel-Bulkley fluids, where the viscosity has a singular part. |
| title | Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids |
| topic | Analysis of PDEs 35Q35, 76N10, 35D30 |
| url | https://arxiv.org/abs/2401.05328 |