6 problems

Weak-profile spectral stability conjecture. If $1<\gamma<3$ and

Let $\bar{s}$ denote the upper bound on the shock speed used in the proof of spectral stability, and suppose $gamma dots$ Wait. Need valid JSON no weird. We need candidate 2 notati…

Let viscous-dispersive shock profile solutions of the quantum hydrodynamics system with linear viscosity be profiles connecting a Lax shock of the underlying Euler system, whose ex…

A nonlinear dispersive equation has a dispersionless solution whose shocks are surrounded by regions of modulated oscillations. Complex-singularity conjecture. These regions can be…

Benjamin–Ono string-equation conjecture. The critical behaviour of solutions to the Benjamin–Ono equation is described by a particular solution of this singular integro-differentia…

Universality conjecture. The critical behaviour at a dispersive shock is universal in this sense.