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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.15410 |
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| _version_ | 1866913950470242304 |
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| author | Bresch, Didier Burtea, Cosmin Szlenk, Maja |
| author_facet | Bresch, Didier Burtea, Cosmin Szlenk, Maja |
| contents | In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously for elliptic equations, stating with the work of Bhattacharya, E. DiBenedetto and J. Manfredi [Rend. Sem. Mat. Univ. Politec. Torino 1989], and more recently for incompressible fluids by J.F. Rodrigues [J. Math. Sciences 2015]. Our result may be seen as an extension to the compressible setting of these previous works. Physically, this is motivated by the fact that the pressures generated during a squeezing flow are often large, potentially requiring the consideration of compressibility, see M. Fang and R. Gilbert [Z. Anal. Anwend 2004]. Mathematically, the main difficulty in the compressible setting concerns the strong hyperbolicparabolic coupling between the density and velocity field. We obtain two main results, the first concerning the one-dimensional non-stationary compressible power-law system while the second one concerns the semi-stationary multi-dimensional case. Finally, we present an extension in onedimension for a viscous Cauchy stress with singular dependence on the shear rate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discontinuous shear-thickening asymptotic for power-law systems related to compressible flows Bresch, Didier Burtea, Cosmin Szlenk, Maja Analysis of PDEs In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously for elliptic equations, stating with the work of Bhattacharya, E. DiBenedetto and J. Manfredi [Rend. Sem. Mat. Univ. Politec. Torino 1989], and more recently for incompressible fluids by J.F. Rodrigues [J. Math. Sciences 2015]. Our result may be seen as an extension to the compressible setting of these previous works. Physically, this is motivated by the fact that the pressures generated during a squeezing flow are often large, potentially requiring the consideration of compressibility, see M. Fang and R. Gilbert [Z. Anal. Anwend 2004]. Mathematically, the main difficulty in the compressible setting concerns the strong hyperbolicparabolic coupling between the density and velocity field. We obtain two main results, the first concerning the one-dimensional non-stationary compressible power-law system while the second one concerns the semi-stationary multi-dimensional case. Finally, we present an extension in onedimension for a viscous Cauchy stress with singular dependence on the shear rate. |
| title | Discontinuous shear-thickening asymptotic for power-law systems related to compressible flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.15410 |