Finite time blow-up for a dyadic model of the Euler equations

By Nets Hawk Katz, Natavsa Pavlovi'c. 2004

110 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e156f8c01961aff28a4b8b068fabc58f507e80da

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

On global attractors of the 3D Navier-Stokes equations (2006, result): “s a weak global attractor, but the existence of a strong global attractor is not known. TNS models have similar form and some similar properties to shell models, specifically dyadic models studied in [10, 14]. Moreover, a similar analysis of the dyadic models also results in a ﬁnite time blow-up (se”
Blow-up in finite time for the dyadic model of the Navier-Stokes equations (2006, methodology): “The dyadic Navier-Stokes equation with hypo-dissipation is written as d dt u+ C(u, u) + ν(∆)u = 0, where we include viscosity ν, which is chosen to be one in [14].”
Dissipative Euler Flows and Onsager's Conjecture (2012, background): “Onsager’s conjecture has also been considered on shell-models [22, 7, 8], whose derivation is motivated by the intuition on locality of interactions.”
Global Attractors of Evolutionary Systems (2006, methodology): “plication of this theorem, which is the existence of a strong global attractor for the inviscid dyadic model of ﬂuid equations introduced b y Friedlander & Pavlovic´ [13] and Katz & Pavlovic´ [16]. This fact is a result of an anomalous dissipation due to the loss of regularity of solutions, ”
Finite time blowup for an averaged three-dimensional Navier-Stokes equation (2014, methodology): “tions may be constructed for ODE systems such as (1.17). Blowup solutions for the equation (1.17) are known to exist for suciently small ; specically, for €1{4 this was (essentially) established in [26], while for €1{3 this was established in [10], with global regularity established in the critical ”