Open AccessStochastic turbulence for Burgers equation driven by cylindrical Lévy process
Author(s) -
Shenglan Yuan,
Dirk Blömker,
Jinqiao Duan
Publication year - 2021
Publication title -
stochastics and dynamics/stochastics and dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.566
H-Index - 26
eISSN - 1793-6799
pISSN - 0219-4937
DOI - 10.1142/s0219493722400044
Subject(s) - mathematics , burgers' equation , inviscid flow , turbulence , mathematical analysis , statistical physics , moment (physics) , flow (mathematics) , white noise , classical mechanics , physics , differential equation , mechanics , geometry , statistics
This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity of solutions and their statistical quantities in this stochastic dynamical system. The quantities include moment estimate, structure function and energy spectrum of the turbulent velocity field. Furthermore, we provide qualitative and quantitative properties of the stochastic Burgers equation when the kinematic viscosity [Formula: see text] tends towards zero. The inviscid limit describes the strong stochastic turbulence.