4 problems

Generic nonexistence conjecture. Entropy-rate-admissible weak solutions possibly do not exist for a generic set of initial data.

Let $u$ be a solution of the grid-function formulation, let $u^{!astphi(u)}{(t,x)}$ denote the associated measure, let $Omega{mathbb{X}}$ be the hyperfinite spatial domain, and le…

Nonuniqueness conjecture. The sequence $u_k$ does not converge, as $k\to\infty$, to the solution of a unique limit problem. More precisely, the mass outside $\Omega$, namely

Let $u$ be an entropy solution to the relevant drift equation, and let $\rho$ be the corresponding solution obtained from $u$ by the scaling change of variables. When a positive tr…