English

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

Analysis of PDEs 2020-04-03 v1

Abstract

The dyadic model u˙n+λ2nunλβnun12+λβ(n+1)unun+1=fn\dot u_n + \lambda^{2n}u_n - \lambda^{\beta n}u_{n-1}^2 + \lambda^{\beta(n+1)}u_nu_{n+1} = f_n, un(0)=0u_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.

Keywords

Cite

@article{arxiv.2004.01074,
  title  = {Non-uniqueness of Leray-Hopf solutions for a dyadic mode},
  author = {Nikolai Filonov and Pavel Khodunov},
  journal= {arXiv preprint arXiv:2004.01074},
  year   = {2020}
}