I am interested in studying fluid dynamics and am searching for a good introductory textbook. I know just the very basics of fluids on the physics side. For mathematical prerequisites, I have completed a course on integration theory, and have a basic understanding of functional analysis and PDE, though by no means am I an expert.

I have done some searching online and most of the books I have come across lean more towards physics, numerical methods, and/or mathematical modeling. What I am instead looking for is something that is more mathematical and analysis/PDE oriented (and ideally one that does not assume too much of this material and introduces it as necessary), targeted towards early graduate students in mathematics. A good example of what I would like are Professor Tao's lecture notes.

Are there any textbooks in this direction?