5 problems

Wild non-uniqueness conjecture. For any such Riemann initial data, there exists a smooth pressure law $p$ with $p'>0$ such that the corresponding system admits infinitely many boun…

Consider the one-dimensional general vacuum initial-value problem with initial sound speed satisfying $\bar c(x)\sim x^{1-\lambda}$ as $x\downarrow 0$, where $\lambda<0$. A local s…

Consider a one-dimensional isentropic Euler flow with fluid initially to the right of the origin, whose initial sound speed decays to zero like $x^{1-\lambda}$ as $x\downarrow 0$,…

Convex-combination representation conjecture. The convex integration scheme should be applicable so that some convex combination of two such weak solutions admits the representatio…

Let $(\rho^0,v^0)$ be the piecewise constant initial data … for the isentropic Euler system with $p(\rho)=\rho^2$, and suppose these data allow the nonuniqueness property of Theore…