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arXiv · 2401.05328

Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids

Cosmin Burtea·Maja Szlenk
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Abstract

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 $\varrho^\gamma$, we construct a solution provided that $r>\frac{3d}{d+2}$ and $\gamma$ 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.

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Cosmin Burtea, Maja Szlenk. 2024-01-10. Weak solutions to the Navier-Stokes equations for steady compressible non-Newtonian fluids. https://arxiv.org/abs/2401.05328

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