Transfer of stochastic energy towards high modes and its application to diffeomorphism flows on tori

Abstract

Dissipativity towards high modes is a classical question in hydrodynamics; for some stochastic model this dissipativity can be exactly computed through the asymptotic of a jump process on the modes; this asymptotical study is the object of this paper.

Anomalous dissipation in a stochastic inviscid dyadic model

“…Its proof is nonstandard; moreover, it is restricted to a range of values of parameters, the generalization being open. Concerning the idea that square moments could satisfy a closed equation, related to jump process, we have been inspired by previous works ( [1,10,11] and [21]), however, devoted to different models; the link here with the nonlinear model and the stochasticity is more transparent via Girsanov's transform.…”

Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold–Ricci tensor

“…The infinitesimal generator of the process η is the matrix M. More elaborated criteria of conservativeness can be developed: we refer to [13].…”