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The recent claim by Grebenev et al. [J. Phys. A: Math. Theor. 50, 435502(2017)] that the inviscid 2D Lundgren-Monin-Novikov (LMN) equations on a zerovorticity characteristic naturally would reveal local conformal invariance whenonly analyzing these by means of a classical Lie-group symmetry approach, isinvalid and will be refuted in the present comment. To note is that within thiscomment the (possible) existence of conformal invariance in 2D turbulence isnot questioned, only the conclusion as is given in Grebenev et al. (2017) andtheir approach how this invariance was derived is what is being criticized andrefuted herein. In fact, the algebraic derivation for conformal invariance ofthe 2D LMN vorticity equations in Grebenev et al. (2017) is flawed. A keyconstraint of the LMN equations has been wrongly transformed. Providing thecorrect transformation instead will lead to a breaking of the proclaimedconformal group. The corrected version of Grebenev et al. (2017) just leads toa globally constant scaling in the fields and not to a local one as claimed. Inconsequence, since in Grebenev et al. (2017) only the first equation within theinfinite and unclosed LMN chain is considered, also different Lie-groupinfinitesimals for the one- and two-point probability density functions (PDFs)will result from this correction, replacing thus the misleading ones proposed.

Conformal invariance and the Lundgren-Monin-Novikov equations for vorticity fields in 2D turbulence: Refuting a recent claim