Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model
Round 1
Reviewer 1 Report
Reviewer Report
In this manuscript, the authors investigated the initial–boundary value problem describing the motion of weakly concentrated aqueous polymer solutions. The model involves the regularized Jaumann’s derivative in the rheological relation. Also this model is considered with non–linear viscosity.
The main result of this paper is the solutions existence to initial–boundary value problem and to the feedback control problem for the mathematical model under consideration. The existence of an optimal solution to the problem under consideration that gives a minimum to a given bounded quality functional is proved.
Since the manuscript reports interesting and important results in the field, my recommendation is to accept it for publication in Polymers Journal, subject to the following minor revision points:
- Authors should discuss in the introduction whether an accurate stochastic models for the analyzed problem can be used and illustrate (cite relevant works) such an alternative approach.
- It would be interesting if authors could mention in the introduction some more relevant works which proposed the various methods for modeling stochastic processes, such as:
- H. Risken, The Fokker-Planck Equation, Berlin: Springer-Verlag, 1989.
- Investigation of mode coupling in graded index plastic optical fibers using the Langevin equation, Journal of Lightwave Technology, Vol. 38, 2020, pp. 6644-6647.
Comments for author File: 
Comments.docx
Reviewer 2 Report
