Blow-up in finite time for the dyadic model of the Navier-Stokes equations

DOI10.1090/S0002-9947-08-04494-2zbMath1156.35073arXivmath/0601074MaRDI QIDQ3533825

Alexey Cheskidov

Publication date: 24 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601074

zbMATH Keywords

regularityenergy estimatesNavier-Stokes equationsglobal attractordyadic model

Mathematics Subject Classification ID

Related Items (28)

On energy cascades in the forced 3D Navier-Stokes equations ⋮ Regularizing effect of the forward energy cascade in the inviscid dyadic model ⋮ On global attractors of the 3D Navier--Stokes equations ⋮ Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity ⋮ Complex singular solutions of the 3-d Navier-Stokes equations and related real solutions ⋮ Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation ⋮ Global regularity for a 3D Boussinesq model without thermal diffusion ⋮ Well Posedness and Limit Theorems for a Class of Stochastic Dyadic Models ⋮ Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations ⋮ Dyadic models for fluid equations: a survey ⋮ Kolmogorov’s dissipation number and determining wavenumber for dyadic models ⋮ Uniqueness of the Leray-Hopf solution for a dyadic model ⋮ Uniqueness and blow-up for a stochastic viscous dyadic model ⋮ Anomalous dissipation in a stochastic inviscid dyadic model ⋮ Self-similar solutions for dyadic models of the Euler equations ⋮ Energy dissipation and self-similar solutions for an unforced inviscid dyadic model ⋮ A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations ⋮ Uniqueness for a stochastic inviscid dyadic model ⋮ A theorem of uniqueness for an inviscid dyadic model ⋮ Finite time blowup for an averaged three-dimensional Navier-Stokes equation ⋮ The vanishing viscosity limit for a dyadic model ⋮ Global attractors of evolutionary systems ⋮ Stochastic Navier-Stokes equations and related models ⋮ Blow-up of a dyadic model with intermittency dependence for the Hall MHD ⋮ Fluid dynamics on logarithmic lattices ⋮ Nonuniqueness of Leray–Hopf solutions for a dyadic model ⋮ Uniqueness and non-uniqueness results for forced dyadic MHD models ⋮ A blow-up result for dyadic models of the Euler equations

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