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Conformal invariance of the probability density function for passive scalar fields (including arbitrary virus) in 2D turbulence: the proof of Polyakov conjecture

Grant number: 21/09845-0
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Duration: October 16, 2021 - April 06, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Alexandre Grichkov
Grantee:Alexandre Grichkov
Visiting researcher: Vladimir Grebenev
Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM


Task 1: Symmetry analysis of the governing equation for the $n$-point PDF $f_n$ for passive scalar fields based on the direct method. Task 2: Conformal invariance of the probability measure. Task 3: The derivation of a Lie group of the symmetry transformations calculated. Task 4: The fine structure of a Lie algebra to classify the zero-isolines by the central charge. Then the effects of non-zero Gaussian white-in-time forcing and large-scale friction along flow surfaces will be included into the consideration. The method and calculations that worked out in (Grebenev, Wac\l{}awczyk and M Oberlack 2017, Wac\l{}awczyk, Grebenev and M Oberlack 2019, (Grebenev, Grishkov, Oberlack, Wac\l{}awczyk 2021) to find symmetries and calculate invariantsof LMN for 2D and 3D vorticity and velocity fields enable us to conclude that this work programme will be successfully completed. It will be published minimum two papers in higher-rank Journals. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GREBENEV, VLADIMIR; GRISHKOV, ALEXANDRE. SLE: differential invariants study. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 16, n. 2, p. 17-pg., . (21/09845-0)

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