Nonuniqueness of Leray-Hopf solutions for a dyadic model. (English. Russian original) Zbl 1464.35178
St. Petersbg. Math. J. 32, No. 2, 371-387 (2021); translation from Algebra Anal. 32, No. 2, 229-253 (2020).
Summary: 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.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 35A24 | Methods of ordinary differential equations applied to PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
systems of ordinary differential equations; Navier-Stokes equations; dyadic model; nonuniqueness of solutionsReferences:
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