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  "body": "\n## Summary\n\nIn the theory of [[conservation laws|8RA7AMWSAF]], a shock wave is a jump discontinuity of a weak solution that moves along a curve in spacetime.\nIts speed is fixed by the [[Rankine–Hugoniot conditions|S4XMYJ3V42]], and an entropy condition decides which jumps are physically admissible.\nShocks form in finite time from smooth data in nonlinear equations such as [[Burgers' equation|NEGHXN8RE1]], so they are unavoidable in the theory.\nThey model the sudden jumps of pressure and density in gas dynamics, such as the shock in front of a supersonic aircraft.\nSee the [[definition|A5GDAAYNM0]].\n\n## Explanations\n\n### L1 human\n\nOn a road, fast cars catch up with slow cars ahead of them, and a sharp edge of a traffic jam forms.\nBehind the edge the traffic is dense, in front of it the road is nearly free, and the edge itself moves.\nThis moving jump is a shock wave.\nFor Burgers' equation with value $1$ on the left and $0$ on the right, the jump moves to the right at speed $1/2$, the average of the two values.\n",
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