On the stochastic selection of integral curves of a rough vector field
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909242348273664 |
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| author | Pitcho, Jules |
| author_facet | Pitcho, Jules |
| contents | We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the vector field constructed by Depauw in [Depauw, C. R. Math. Acad. Sci. Paris, 2003], which lies in the above class, and prove that for this vector field, the unique incompressible measure on integral curves exhibits stochasticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stochastic selection of integral curves of a rough vector field Pitcho, Jules Analysis of PDEs Classical Analysis and ODEs Probability 34A99, 35C99, 60G99 We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the vector field constructed by Depauw in [Depauw, C. R. Math. Acad. Sci. Paris, 2003], which lies in the above class, and prove that for this vector field, the unique incompressible measure on integral curves exhibits stochasticity. |
| title | On the stochastic selection of integral curves of a rough vector field |
| topic | Analysis of PDEs Classical Analysis and ODEs Probability 34A99, 35C99, 60G99 |
| url | https://arxiv.org/abs/2407.02364 |