Non-uniqueness of Hölder continuous solutions for Inhomogeneous Incompressible Euler flows
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909925820596224 |
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| author | Giri, Vikram Koley, Ujjwal |
| author_facet | Giri, Vikram Koley, Ujjwal |
| contents | We consider the inhomogeneous (or density dependent) incompressible Euler equations in a three-dimensional periodic domain. We construct density $\varrho$ and velocity $u$ such that, for any $α<1/7$, both of them are $α$-Hölder continuous and $(\varrho, u)$ is a weak solution to the underlying equations. The proof is based on typical convex integration techniques using Mikado flows as building blocks. As a main novelty with respect to the related literature, our result produces a Hölder continuous density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness of Hölder continuous solutions for Inhomogeneous Incompressible Euler flows Giri, Vikram Koley, Ujjwal Analysis of PDEs We consider the inhomogeneous (or density dependent) incompressible Euler equations in a three-dimensional periodic domain. We construct density $\varrho$ and velocity $u$ such that, for any $α<1/7$, both of them are $α$-Hölder continuous and $(\varrho, u)$ is a weak solution to the underlying equations. The proof is based on typical convex integration techniques using Mikado flows as building blocks. As a main novelty with respect to the related literature, our result produces a Hölder continuous density. |
| title | Non-uniqueness of Hölder continuous solutions for Inhomogeneous Incompressible Euler flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.15884 |