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  "body": "\n## Summary\n\nAn entropy solution of a scalar conservation law $u_t + \\operatorname{div} f(u) = 0$ is a [[weak solution|SJZX81A783]] that also satisfies a family of inequalities, the entropy conditions.\nWeak solutions of conservation laws are in general not unique, because shocks can be drawn in many ways.\nThe entropy conditions select the physically relevant solution, the one obtained as the limit of solutions with small added viscosity.\nIn Kruzhkov's formulation, the entropy solution of the initial value problem exists and is unique for every bounded initial datum.\n\n## Explanations\n\n### L1 human\n\nSolutions of conservation laws, such as models of traffic or gas flow, develop jumps called shocks even from smooth initial data.\nOnce jumps are allowed, the equation alone permits several solutions, some of them unphysical, like a shock that spontaneously forms from a smooth spreading wave.\nThe entropy condition is an extra rule saying that information may only flow into a shock, never out of it.\nFor Burgers' equation $u_t + (u^2/2)_x = 0$, a jump from $1$ down to $0$ is allowed, while a jump from $0$ up to $1$ must instead spread out into a fan.\n",
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