There are many problems relating to stretching or squeezing of sheet in which we obtain a dimensionless parameter which contains "x" or "t", symbolizing a local behaviour of the parameter on the flow. How is this justified?
T. H. Ray
Tanya Sharma
A most interesting question.
If I understand it correctly. I'll risk answering that one needs an extra dimension to justify the dimensionless point. Lifting the analysis to 3 dimensions yields a result like Perelman's proof of the Thurston Geometrization Conjecture, in which Ricci flow with surgery becomes extinct in finite time.
https://arxiv.org/pdf/math/0610903v1.pdf
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Abdulkafi Mohammed Saeed
I suggested to read this file
http://www.pmt.usp.br/ACADEMIC/martoran/NotasModelosGrad/Dimensional%20Analysis.pdf
All the best
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