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

2020/04/02 by N. Filonov, Filonov, Nikolai, Pavel Khodunov +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.01074

openalex publication_date 2020/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The dyadic model u_n + λ²ⁿu_n - λ^βnu_n-1² + λ^β(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.

Related

• Uniqueness of the Leray-Hopf solution for a dyadic model
• Uniqueness and non-uniqueness results for dyadic MHD models
• Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model
• Well Posedness for Positive Dyadic Model
• Uniqueness for a Stochastic Inviscid Dyadic Model