On Averaging and Mixing for Stochastic PDEs is mixing, then the convergence is uniform in time. © The Author(
s), under exclusive licence to Springer
Weak and Strong Versions of the Kolmogorov 4/5-Law for Stochastic Burgers Equation universality of Kolmogorov’
s theory of turbulence, and show that the third moment is the only one which admits
A refinement of Heath-Brown’s theorem on quadratic formsA refinement of Heath-Brown’
s theorem on quadratic forms
The K41 theory and turbulence in 1D Burgers equation to turbulence, known as the K41 theory. The presentation is based on the recent book by Boritchev and
Kuksin Averaging and mixing for stochastic perturbations of linear conservative systems=\varepsilon P(v(t)) dt+\sqrt{\varepsilon} \mathcal{
B}(v(t)) dW (t), \qquad v\in\mathbb{R}^D, \tag{*} \end
Formal Expansions in Stochastic Model for Wave Turbulence 2: Method of Diagram Decomposition, driven by a random force [the study was initiated in our previous work Dymov and
Kuksin (Commun Math Phys