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The current claim by Grebenev et al. [J. Phys. A: Math. Theor. 52, 335501(2019)], namely that the inviscid and unclosed 2D Lundgren-Monin-Novikov (LMN)equations on a zero-vorticity Lagrangian path admit conformal invariance, isbased on a flawed and misleading analysis published earlier by Grebenev et al.(2017). All false results and conclusions made before in the Eulerian picturewere now extended by Grebenev et al. (2019) to the Lagrangian picture. Althoughwe have already commented on these errors and consistently refuted theirprevious study (Frewer & Khujadze, 2018), we deem it necessary to address anddiscuss these errors again in the new formulation and notation of Grebenev etal. (2019) as it will offer new insights into this issue.

Comment on 'Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence'