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arXiv · 2004.01074

Non-uniqueness of Leray-Hopf solutions for a dyadic mode

Nikolai Filonov·Pavel Khodunov
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Abstract

The dyadic model $\dot u_n + \lambda^{2n}u_n - \lambda^{\beta n}u_{n-1}^2 + \lambda^{\beta(n+1)}u_nu_{n+1} = f_n$, $u_n(0)=0$, is considered. It is shown that in the case of non-trivial right hand side the system can have two different Leray-Hopf solutions.

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Nikolai Filonov, Pavel Khodunov. 2020-04-02. Non-uniqueness of Leray-Hopf solutions for a dyadic mode. https://arxiv.org/abs/2004.01074

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