Weak solutions to the steady incompressible Euler equations with source terms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909201613193216 |
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| author | Huang, Anxiang |
| author_facet | Huang, Anxiang |
| contents | In this paper, we prove the non-uniqueness of stationary solutions to steady incompressible Euler equations with source terms. Based on the convex integration scheme developed by De Lellis and Székelyhidi, the Euler system is reformulated as a differential inclusion. The key point is to construct the corresponding plane-wave solutions via high frequency perturbations. Then we use iteration and Baire category argument to conclude that there exist a large amount of weak solutions with given energy profile. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak solutions to the steady incompressible Euler equations with source terms Huang, Anxiang Analysis of PDEs 76B03 35D05 In this paper, we prove the non-uniqueness of stationary solutions to steady incompressible Euler equations with source terms. Based on the convex integration scheme developed by De Lellis and Székelyhidi, the Euler system is reformulated as a differential inclusion. The key point is to construct the corresponding plane-wave solutions via high frequency perturbations. Then we use iteration and Baire category argument to conclude that there exist a large amount of weak solutions with given energy profile. |
| title | Weak solutions to the steady incompressible Euler equations with source terms |
| topic | Analysis of PDEs 76B03 35D05 |
| url | https://arxiv.org/abs/2405.08390 |