Weak solution for granular model
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912389518065664 |
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| author | Chupin, Laurent Dubois, Thierry |
| author_facet | Chupin, Laurent Dubois, Thierry |
| contents | This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as the dilatance effects. It is the coupling of these two physical phenomena that ensures stability and the existence of dissipated energy. The key point of the article is to understand how this energy can ensure the existence of a weak solution. We first establish a complete result on a simplified model, then demonstrate how it can be extended to more general cases. This work represents a real breakthrough in the mathematical analysis of this type of models for complex flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak solution for granular model Chupin, Laurent Dubois, Thierry Analysis of PDEs Classical Physics This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as the dilatance effects. It is the coupling of these two physical phenomena that ensures stability and the existence of dissipated energy. The key point of the article is to understand how this energy can ensure the existence of a weak solution. We first establish a complete result on a simplified model, then demonstrate how it can be extended to more general cases. This work represents a real breakthrough in the mathematical analysis of this type of models for complex flows. |
| title | Weak solution for granular model |
| topic | Analysis of PDEs Classical Physics |
| url | https://arxiv.org/abs/2505.17588 |