This article deals with a survey of the Newtonian fluid dynamics equations with some historical notes and a discussion related to the solvability of fluid flows problems. On the way, we discuss briefly various questions related with the behavior of fluid flows governed by these fluid dynamics equations. Some of these questions are, in fact, closely connected with the well-posedness of fluid dynamics problems. We touch on the problem of the fluid dynamics limit of the Boltzmann equation of the kinetic theory of gases. An overview of some rigorous recent results on the existence and uniqueness of solutions of the fluid flows problems concludes this paper. At the end, after some concluding remarks, there are 306 references.

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