Non-Uniqueness and Inadmissibility of the Vanishing Viscosity Limit of the Passive Scalar Transport Equation

Lucas Huysmans, Edriss S. Titi

We study selection by vanishing viscosity for the transport of a passive scalar $f(x,t)\in \mathbb{R}$ advected by a bounded, divergence-free vector field $u(x,t)\in {\mathbb{R}}^2$. T…