Euler equations

The Euler equations describe the motion of an idealized fluid with no viscosity, relating changes in velocity and pressure to applied forces.

Navier–Stokes equations: The equations of fluid motion that include viscous stresses as well as pressure and external forces. Setting viscosity to zero in this model yields the Euler equations.
Fluid mechanics: The study of fluids at rest and in motion, including forces, flow, and transport. The Euler equations are a central mathematical model within this broader field.
Potential flow: An idealized flow with zero vorticity that can be represented by a velocity potential. It is a tractable Euler-flow model around bodies away from viscous boundary layers.
Kelvin's circulation theorem: A theorem stating that circulation around a material loop remains constant in an inviscid barotropic flow with conservative body forces. It follows from Euler dynamics under these assumptions and constrains vortex evolution.
Leonhard Euler: An eighteenth-century Swiss mathematician whose work shaped mechanics, analysis, and fluid dynamics. Euler formulated the ideal-fluid motion equations that bear his name.
Continuity equation: A conservation law stating that changes in density are balanced by the flow of mass. It supplies mass conservation alongside momentum conservation in the fluid equations.
Inviscid flow: Fluid motion modeled without internal friction or viscous stresses. This is the defining physical idealization behind the equations.
Shock wave: A thin moving discontinuity across which pressure, density, and velocity change sharply. Compressible Euler equations describe shock motion through conservation laws.
Vorticity equation: An evolution equation for the local rotation of a fluid, represented by the curl of velocity. Taking the curl of the Euler momentum equation gives its inviscid form.
Isaac Newton: An English mathematician and physicist who formulated classical laws of motion and universal gravitation. Euler's fluid momentum balance applies Newton's second law to fluid elements.

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