Energy dissipation and self-similar solutions for an unforced inviscid dyadic model

DOI10.1090/S0002-9947-2010-05302-4zbMath1301.37061arXiv0811.1689OpenAlexW2040895392MaRDI QIDQ2997223

Francesco Morandin, David Barbato, Franco Flandoli

Publication date: 6 May 2011

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

Full work available at URL: https://arxiv.org/abs/0811.1689

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Fundamentals of turbulence (76F02) Self-similar solutions to PDEs (35C06)

Related Items (16)

Regularizing effect of the forward energy cascade in the inviscid dyadic model ⋮ Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity ⋮ Well Posedness and Limit Theorems for a Class of Stochastic Dyadic Models ⋮ Dyadic models for fluid equations: a survey ⋮ 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 ⋮ A dyadic model on a tree ⋮ Uniqueness for a stochastic inviscid dyadic model ⋮ A theorem of uniqueness for an inviscid dyadic model ⋮ Stochastic Navier-Stokes equations and related models ⋮ Blow-up of a dyadic model with intermittency dependence for the Hall MHD ⋮ Uniqueness and non-uniqueness results for forced dyadic MHD models ⋮ A blow-up result for dyadic models of the Euler equations ⋮ Dyadic models for ideal MHD

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• Statistical properties of nonlinear shell models of turbulence from linear advection models: rigorous results
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