It is the study of the behavior of fluids: liquids, gases, blood, plasmas. The most important equations in this field are the Navier-Stokes equations.
Approach to fluids: is based on Continuum Mechanics, and a good introduction to the notion of fluid can be read here.
Once it is understood what is a fluid, there are two approach to the description: Eulerian and Lagrangian approaches.
"The Lagrangian perspective is a natural way to describe the motion of solid objects. For example, suppose an apple falls from a tree. Newton taught us to describe the height and velocity _of the apple_ as functions of time. This is a Lagrangian description. To try to describe this event in terms of Eulerian fields would be very awkward. You might define A(z,t) as the “appliness”: A = 1 at points in space and time occupied by the apple and 0 everywhere else, then try to derive a differential equation for A" (extracted from here.
Important notions:
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Author of the notes: Antonio J. Pan-Collantes
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