6 problems

The von Neumann sonic conjecture. There exists a supersonic regular shock reflection-diffraction configuration when

A tame solution of the Euler–Poisson system with vacuum may be nonsymmetric. Makino's conjecture. Any tame solution, including a nonsymmetric tame solution, will become not tame af…

For the multi-dimensional compressible Navier–Stokes–Korteweg system under consideration, let $\rho$ denote the density, $u$ the velocity, $N\in\{2,3\}$ the spatial dimension, and…

DiPerna's conjecture. All $\prec_{DiP}$ maximal solutions are weak solutions; equivalently, their energy defect vanishes for almost every time.

Slemrod's conjecture. The energy dissipation obtained when the compressible Euler equations are viewed from the perspective of kinetic theory has additional terms relative to the e…

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…