Non-Newtonian compressible fluids with stochastic right hand side
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908340082180096 |
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| author | Ludvík, Pavel Mácha, Václav |
| author_facet | Ludvík, Pavel Mácha, Václav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Newtonian compressible fluids with stochastic right hand side Ludvík, Pavel Mácha, Václav Analysis of PDEs 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. |
| title | Non-Newtonian compressible fluids with stochastic right hand side |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.19360 |