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

• 主讲人：Sergei Kuksin (Steklov Mathematical Institute of RAS)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2023-03-10 17:00 - 2023-03-10 18:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/75E4F78ABA835368BBC9736011785A8E
Valid Until: 2027-04-30 23:59

 

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.

 

Bio: Sergey Kuksin is a Leading Scientific Researcher at Steklov Mathematical Institute of RAS, a Senior Researcher at the Mathematics Institute of Jussieu–Paris Rive Gauche and a Professor at Heriot-Watt University. He became Doctor of Sciences from Lomonosov Moscow State University in 1981. Kuksin’s research deals with KAM theory in PDE. He was an invited speaker of ICM 1998 in Berlin. In 2016, he received Lyapunov Award from the Russian Academy of Sciences.