8 problems

Subsonic-or-sonic stability conjecture. A standing or traveling wave profile for the QHD systems with linear or nonlinear viscosity is spectrally stable if and only if its velocity…

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

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…

Vacuum-boundary characterization conjecture. The measure $\tilde\lambda$ might be a useful tool to characterize the behaviour of vacuum boundaries or other functions, such as the p…

Consider chiral flows in vortex fluids within the proposed correspondence between large-$N$ supersymmetric gauge theories and integrable $1+1$-dimensional hydrodynamics. Vortex-flu…

The paper considers dimensional transmutation in $1+1$-dimensional quantum hydrodynamics, with chiral flows arising in vortex fluids such as rotating superfluids and fractional qua…

Consider the repulsive Lieb-Liniger model, whose low-energy effective hydrodynamic description is given by the quantum Korteweg–de Vries equation. Its excitations include Lieb's ty…

Consider the one-dimensional quantum hydrodynamic system … for $t>0$ and $x\in[0,1]$, with positive initial density, the Neumann conditions $\rho_x(0,t)=\rho_x(1,t)=0$, and boundar…