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  "body": "\n## Summary\n\nThe Cahn–Hilliard equation is the fourth-order parabolic equation $c_t = \\Delta(c^3 - c - \\gamma \\Delta c)$.\nIt describes how a mixture of two substances separates into regions rich in one or the other.\nUnlike the [[Allen–Cahn equation|7S813PEV69]], it conserves the total amount $\\int c\\,dx$.\nIt is the gradient flow of the Ginzburg–Landau energy in the $H^{-1}$ metric.\n\n## Explanations\n\n### L1 human\n\nShake oil and vinegar together, then let the mixture rest: droplets form and slowly grow.\nThe Cahn–Hilliard equation models this.\nThe concentration $c$ is near $+1$ in one substance and near $-1$ in the other.\nMatter is only moved around, never created, so the average of $c$ stays fixed while the pattern coarsens.\n",
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