Functional Analysis for Differential Equations: Entry-Level Guide

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The discussion centers on finding an entry-level book that bridges the gap between theoretical mathematics and practical applications of functional analysis in differential equations, specifically the Navier-Stokes equation and PDEs in general. The user expresses frustration with existing resources, which are either overly mathematical or too focused on physics without adequate mathematical context. A recommended resource is "Applied Analysis" by J. Hunter, which is noted for being accessible and free, making it a suitable choice for those seeking a balanced approach to the subject.
Andy Resnick
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I'm looking for a entry-level book discussing the application of functional analysis to differential equations- mostly the Navier-Stokes equation, but PDEs in general. The books I have or have seen are either math books, full of proofs and definitions without application, or physics papers which use the concepts (sequences, norms, Banach spaces,etc) without any clear motivation or discussion of the mathematics. I need something in between the two.

Any advice is appreciated, thanks in advance.
 
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