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arXiv · 2510.05990

Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids

Francesca Crispo·Angelica Pia Di Feola·Carlo Romano Grisanti
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Abstract

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 $v_0\in J^2(\Omega)$ 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.

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Francesca Crispo, Angelica Pia Di Feola, Carlo Romano Grisanti. 2025-10-07. Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids. https://arxiv.org/abs/2510.05990

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