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arXiv · 2407.15884

Non-uniqueness of H\"older continuous solutions for Inhomogeneous Incompressible Euler flows

Vikram Giri·Ujjwal Koley
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Abstract

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 $\alpha<1/7$, both of them are $\alpha $-H\"older 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 H\"older continuous density.

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Vikram Giri, Ujjwal Koley. 2024-07-21. Non-uniqueness of H\"older continuous solutions for Inhomogeneous Incompressible Euler flows. https://arxiv.org/abs/2407.15884

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