Nonuniqueness of Leray–Hopf solutions for a dyadic model

Filonov, N.; Khodunov, P.

doi:10.1090/spmj/1651

Nonuniqueness of Leray–Hopf solutions for a dyadic model
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by N. Filonov and P. Khodunov
Translated by: P. Khodunov

St. Petersburg Math. J. 32 (2021), 371-387

DOI: https://doi.org/10.1090/spmj/1651

Published electronically: March 2, 2021

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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 nontrivial right-hand side the system may have two different Leray–Hopf solutions.

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