The Navier-Stokes Equations

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Focusing on the mathematical theory of viscous incompressible fluids, this monograph presents a self-contained approach using Navier-Stokes equations in various domains of Euclidean space. Aimed at students with a foundational understanding of functional analysis, it begins with essential properties of Sobolev spaces and operators. The text formulates theory applicable to general, potentially unbounded, non-smooth domains, particularly in two and three dimensions. It addresses a gap in systematic treatments of this functional-analytic approach, despite the extensive existing literature.