12 problems

Vanishing viscosity conjecture. The entropic solutions of the hyperbolic system (1.1) actually coincide with the limits of solutions to the parabolic system

The paper considers the hyperbolic Keller–Segel system with time-dependent parameters and its global strong solutions in the critical Besov space…

Let solutions of a $2\times2$ system of conservation laws have initial data with small oscillation, meaning that the data are close in $\mathbf L^\infty$ to a constant. The Glimm–L…

Scalar-field estimate conjecture. The scalar matter field obeys a similar estimate with integrand $P^2$. The scalar matter field decouples from the metric perturbations in the line…

Let the initial-boundary value problem for the Einstein equations be linearised about a background spacetime, and let a Bondi-like gauge mean a gauge in which coordinate lines of c…

Let $N\times N$ be the computational grid, and let the solution be computed using a forward discrete Radon transform (DRT), a one-dimensional local time-stepping (LTS) method, and…

Equality conjecture. In every cell of Table 1, except possibly the cell corresponding to $X_9^2$, each inequality can be replaced by an equality.

The methods concern evaluating far-field signals for time-domain wave propagation. In particular, consider linear hyperbolic systems which, apart from inhomogeneities, are time ind…

Majda's conjecture. Smooth initial data for weakly nonlinear systems do not break in finite time. This conjecture concerns finite-time breakdown and global smoothness for linearly…

Positivity conjecture. For all $\kappa>0$, we have $0<\widetilde c(\kappa)<c(\kappa)$. Consequently, in the SOH model, we have $\delta>0$, and the SOH model is well-posed if it is…

Kinetic equation of state hyperbolicity and causality conjecture. Under this equation of state, there exists a smooth function $f_{\rm kinetic}$ such that

For modes indexed by $n$, let $n_c$ satisfy … with the non-generic integer case excluded. For subcritical modes $1\leq n<n_c$, impose … … For supercritical modes $n>n_c$, impose ……