An older, classic text is Mathematical Theory of Compressible Fluid Flow by Richard von Mises. More recent text books include Introduction to Mathematical Fluid Dynamics by R.E. Meyer. An Introduction to Theoretical Fluid Dynamics by S. Childress. A Mathematical Introduction to Fluid Mechanics by A.J. Chorin and J.E. Marsden.
A few possibilities: JC Robinson, JL Rodrigo, & W Sadowski (2016) Classical theory of the three-dimensional Navier-Stokes equations. OA Ladyzhenskaya (1963) The mathematical theory of viscous incompressible flow.
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…
You can get the free ~900 pages book Genick Bar-Meir, Basics of Fluid Mechanics , https://zenodo.org/records/8184518 or this one on compressible flow: Genick Bar-Meir, Fundamentals of Compressible Fluid Mechanics , https://zenodo.org/records/6467559 Good luck
