Anomalous dissipation in a stochastic inviscid dyadic model

Barbato, Davide; Flandoli, Franco; Morandin, Francesco

doi:10.1214/11-aap768

Cited by 20 publications

(46 citation statements)

References 25 publications

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“…Even if the motivations for these models are quite different, it is also natural to see the tree models as generalizations of the usual shell models. This has been done for example by Benzi and Biferale for the GOY model in [15] and in [4] for many results that were proved about the dyadic in [6].…”

Section: Introductionmentioning

confidence: 99%

Structure Function and Fractal Dissipation for an Intermittent Inviscid Dyadic Model

Bianchi

Morandin

2017

Commun. Math. Phys.

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We study a generalization of the original tree-indexed dyadic model by Katz and Pavlović for the turbulent energy cascade of three-dimensional Euler equation. We allow the coefficients to vary with some restrictions, thus giving the model a realistic spatial intermittency. By introducing a forcing term on the first component, the fixed point of the dynamics is well defined and some explicit computations allow to prove the rich multifractal structure of the solution. In particular the exponent of the structure function is concave in accordance with other theoretical and experimental models. Moreover anomalous energy dissipation happens in a fractal set of dimension strictly less than 3.

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Section: Introductionmentioning

confidence: 99%

Structure Function and Fractal Dissipation for an Intermittent Inviscid Dyadic Model

Bianchi

Morandin

2017

Commun. Math. Phys.

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“…Let us finally mention two works on anomalous dissipation (very related to the issues treated here) in a stochastic setting similar to the one treated in this Chapter: Mattingly et al [158], Barbato et al [23]. Let us finally mention two works on anomalous dissipation (very related to the issues treated here) in a stochastic setting similar to the one treated in this Chapter: Mattingly et al [158], Barbato et al [23].…”

Section: Preliminary Remarksmentioning

confidence: 87%

Random Perturbation of PDEs and Fluid Dynamic Models

Flandoli

2011

Lecture Notes in Mathematics

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175

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It is intended for PhD students, teachers and researchers who are interested in probability theory, statistics, and in their applications.The duration of each school is 13 days (it was 17 days up to 2005), and up to 70 participants can attend it. The aim is to provide, in three highlevel courses, a comprehensive study of some fields in probability theory or Statistics. The lecturers are chosen by an international scientific board. The participants themselves also have the opportunity to give short lectures about their research work.Participants are lodged and work in the same building, a former seminary built in the 18th century in the city of Saint-Flour, at an altitude of 900 m. The pleasant surroundings facilitate scientific discussion and exchange.

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“…We are left to prove existence for the infinite dimensional system (2). We will obtain the result by means of Ascoli-Arzelà theorem and a standard diagonal argument.…”

Section: Existencementioning

confidence: 99%

“…Moreover, this solution is unique if, given two solutions u (1) and u (2) with the same initial condition, it holds u (1) (t) = u (2) (t) for all t ∈ [0, T ] a.s..…”

Section: Strong Solutionsmentioning

confidence: 99%