= Viscous stability of an accretion disk
{title2=$\partial_\Sigma(\bar\nu\Sigma)>0$}
Within an instantaneous vertically averaged transport closure, the local <Keplerian viscous diffusion equation> has effective diffusion coefficient $3\partial_\Sigma(\bar\nu\Sigma)$. A positive coefficient smooths short radial <Fourier modes> in the allowed thin-disc wavelength range; a negative coefficient gives the <negative-diffusion criterion for viscous disk instability>. A zero coefficient is linearly degenerate and does not establish strict decay. This local response criterion alone does not settle thermal, self-gravitating or boundary-driven stability.
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