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  "body": "\n## Summary\n\nThe Euler equations describe the motion of an ideal fluid, that is, a fluid without viscosity.\nThey express conservation of mass and Newton's second law for each parcel of fluid, with pressure as the only internal force.\nThe incompressible Euler equations are the case $\\nu = 0$ of the [[Navier–Stokes equations|18KXZHVF4M]].\nThey were among the first partial differential equations written down, and many questions about them are still open.\n\n## Explanations\n\n### L1 human\n\nImagine a fluid with no internal friction at all, so that layers can slide past each other freely.\nEach small parcel of such a fluid is pushed only by differences in pressure around it.\nThe Euler equations state this, together with the rule that fluid is neither created nor destroyed.\nA simple example is water spinning as a rigid body in a bucket: the velocity is $(-y, x, 0)$ and the pressure grows like $(x^2 + y^2)/2$ away from the axis.\nThat higher pressure at the rim is what bends the water surface into a curve.\n",
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