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Beijing–Moscow Mathematics Colloquium
March 10, 2023 12:00, Moscow, online


Kolmogorov's theory of turbulence, the Landau criticism and their rigorous 1d versions

S. B. Kuksin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Kolmogorov's theory of turbulence contains two celebrated heuristic laws, related to the second and third moments of increments of the fluid's velocity field $u(t,x+r)-u(t,x)$ for "small but not too small $r$". Kolmogorov claimed that the moments as functions of $r$ have the form (universal pre-factor) $x$ (certain exponent of $|r|$). Landau's criticism was that the pre-factor indeed may be universal for the third moment, but not for the second. In my talk, I will explain that the two heuristic laws allow rigorous versions, related to a fictitious one-dimensional fluid, described by the Burgers equation. There - indeed - the pre-factor in the law for the third moment is explicit and universal, but that for the second moment cannot be such. I will explain the difference between the two moments which leads to this effect.

Language: English


© Steklov Math. Inst. of RAS, 2024