10 problems

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…

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

The Euler equations describe compressible inviscid flow, and a carbuncle is a numerical instability associated especially with methods based on Riemann solvers. Robinet, Gressier,…

Let $\Delta x$ and $\Delta t$ denote the spatial and temporal mesh sizes, respectively, and consider approximate solutions obtained by replacing space and time derivatives in the e…

Let $\Omega$ be the computational domain, let $\Gamma_- = \{\mathbf x\in\Gamma: \mathbf v(\mathbf x)\cdot\mathbf n(\mathbf x)<0\}$ be the inflow part of the boundary, let…

Hypersonic similarity convergence conjecture. As $\tau$ becomes small, the solutions of the full Euler problem should converge to the solution in $\Omega$ of the hypersonic small-d…

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…

The regularized Euler evolution equations for density $\rho$, momentum density $u_i$, entropy density $s$, pressure $p$, and velocity $v_i=u_i/\rho$ are given by the displayed syst…

Compressible potential flow is described by a conservation-law system for the density $\varrho$ and velocity $\mathbf v$, with entropy weak solutions understood in the usual distri…

The three-dimensional nozzle problem prescribes the incoming flow angles $\frac{u_2}{u_1}$ and $\frac{u_3}{u_1}$ and Bernoulli's function $B$ at the inlet, together with the end pr…