Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916994732785664 |
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| author | Crispo, Francesca Di Feola, Angelica Pia Grisanti, Carlo Romano |
| author_facet | Crispo, Francesca Di Feola, Angelica Pia Grisanti, Carlo Romano |
| contents | The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data $v_0\in J^2(Ω)$ and for $p\in \left(\frac 95,2\right)$. It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids Crispo, Francesca Di Feola, Angelica Pia Grisanti, Carlo Romano Analysis of PDEs Mathematical Physics The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data $v_0\in J^2(Ω)$ and for $p\in \left(\frac 95,2\right)$. It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities. |
| title | Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2510.05990 |