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arXiv · 2504.19360

Non-Newtonian compressible fluids with stochastic right hand side

Pavel Ludvík·Václav Mácha
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Abstract

Fluids with shear-rate-dependent viscosity form a special class of non-Newtonian fluids that play a crucial role in continuum dynamics. We consider a compressible barotropic flow of such fluids, governed by a generalized Navier-Stokes system. Due to the nonlinearity in the elliptic term, obtaining the existence of a weak solutions is challenging. To address this, we introduce the concept of a measure-valued solution, whose existence is established in a very general setting using an abstract theorem on the existence of a Young measure. We also discuss the proof of this key result.

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Pavel Ludvík, Václav Mácha. 2025-04-27. Non-Newtonian compressible fluids with stochastic right hand side. https://arxiv.org/abs/2504.19360

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