I've recently been interested in the Navier-Stokes equations. I would like to understand them deeply from a mathematical point of view.
What courses in advanced mathematics (and physics?), and in what order, should I take in order to understand the Navier-Stokes equations and eventually understand scientific papers on Navier-Stokes existence and smoothness problem?
I've found this Math.SE question but it asks about references in general, whereas I'm asking about specific undergraduate and graduate level courses. Let's assume for the purpose of this question that I am an undergraduate mathematics student who can focus 100% of his studies only on understanding the Navier-Stokes equations. Note that I am asking for a typical academic courses and that I'm especially interested in the sequence/order of the courses.
EDIT: As for me specifically, I've taken courses in Mathematical analysis, as well as Geometry and linear algebra so far (as well as some introductory courses in computational mathematics and computer science).