A Mathematical Introduction to Fluid Mechanics

This study presents some selected highlights of current topics in fluid mechanics in a compact form, as well as providing a concise exposition of the basic theory of fluid mechanics.

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This study presents some selected highlights of current topics in fluid mechanics in a compact form, as well as providing a concise exposition of the basic theory of fluid mechanics. The first chapter contains an elementary derivation of the equations, and the concept of vorticity is introduced. The second chapter contains a discussion of potential flow, vortex motion and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented. The text also contains an analysis of one-dimensional gas flow, weak solutions, Riemann problems, Glimm's scheme and combustion waves.