31 problems

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

Let $\theta_{\rm w}^{\rm d}$ be the detachment angle, and let state (2) be the weak or strong uniform state satisfying the local shock conditions for a wedge angle…

Let a nonlinear symmetric hyperbolic system in $n$ spatial dimensions have totally linearly degenerate structures. Suppose a smooth solution belongs to … with $s>\frac{n}{2}+1$. Ma…

Structural stability conjecture. It is conjectured that the steady Mach reflection in $\mathbb{R}^2$ is structurally stable.

Let the one-dimensional flow model have particle trajectories governed by $dx/dt=v=-H(\theta)$, where $H(\theta)$ is antisymmetric, so that a particle initially at the origin remai…

The model uses an FRW equation of state intended to agree with that of the standard cosmological model after radiation decouples from matter. Uniform-expansion conjecture. If the e…

Universal Jouguet applicability conjecture. The newly formulated condition derived from comparing the second derivatives of the $\mathcal U$-characteristics and the chemical shock…

Let a shock hypersurface be a hypersurface across which a weak solution develops a shock in a quasilinear wave equation posed in multiple spatial dimensions. Dynamic singularity fo…

Let a weakly stable shock wave arise in isentropic elastodynamics. Weak-shock structural stability conjecture. Weakly stable shock waves in isentropic elastodynamics are structural…

Consider the nonlinear hyperbolic system, with shocks parameterized along the positive part of their shock curves. The authors refer to shocks satisfying a moderate shock size cond…

Consider the cubic Burgers equation with flux $f(u)=u^3$ and Riemann initial data $u_-$ and $u_+$. If $u_-<0$ and … or if $u_->0$ and … then the inviscid Riemann solution consists…

Scaling-law persistence conjecture. The scaling laws proven for smooth flux functions remain true for locally Lipschitz continuous flux functions such as the modular Burgers' equat…

Let the Friedmann–Robertson–Walker metric be perturbed by self-similar perturbations, and suppose the cosmological constant is absent. Self-similar acceleration conjecture. Certain…

For a numerical scheme, let the mass flux denote its mass-flux function and let the pressure term denote the pressure contribution to that flux. Liou's conjecture. Schemes with a m…

A Guderley solution is a radial self-similar solution of the Euler system, defined at least for all negative times, with a converging shock propagating into a quiescent fluid near…

Let $\sigma$ and $\bar{\sigma}$ be equation-of-state parameters, and let $a$ be a positive acceleration parameter. The notation FLRW$(0,\sigma,a)$ denotes a Friedmann–Lemaître–Robe…

A Friedmann-static shock wave has an interior described by an FLRW$(0,\sigma,a)$ spacetime, where $\sigma$ is the equation-of-state parameter and $a$ is the acceleration parameter.…

Consider regular shock reflection-diffraction configurations with wedge angle $\theta_{\rm w}\in (\theta_{\rm w}^{\rm d},\frac{\pi}{2})$, including the weak and strong configuratio…

Let $q^w$ and $q^z$ be the good unknowns satisfying … Let $\mathfrak{s}_2$ denote the shock curve, and interpret $C^{1,\frac{1}{2}}$ as the corresponding Hölder regularity across t…

BDN generalization conjecture. The phenomena established in this note should have counterparts in generalizations of the original BDN model to other fluids.

Consider a wide class of gas-dynamic models with conservative regularization, including the one-dimensional R-gas dynamics discussed here. A steady shock-like solution is a station…

Periodic nonsingularity conjecture. In a periodic domain, there exist nontrivial solutions in which no singularity forms.

For $\rho$ the density and $u=(u_r,u_\uptheta)$ the velocity solving the two-dimensional isentropic compressible Euler equations, suppose the solution constructed in Theorem genera…

A steady supersonic flow impinges onto a solid wedge whose angle is less than a critical angle, namely the detachment angle. Shock polar analysis yields two possible steady configu…

Let a shock-wave spacetime have a metric that is Lipschitz continuous, with bounded connection and curvature, and let an optimal coordinate system mean one in which the metric conn…