11 problems

Cauchy-horizon conjecture. The perturbed solution has a Cauchy horizon that is a perturbation of the Cauchy horizon of the background solution.

Crease-and-singular-boundary conjecture. The perturbed solution has a crease and singular boundary that are perturbations of the crease and singular boundary of the background solu…

Time-of-first-blowup conjecture. The perturbed solution forms a shock at a time that is a perturbation of $T_{\mathrm{Shock}}$; its first blowup time is the smallest value of $t$ a…

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

Under the relations referred to in the source as equations … , let $p$ be the pressure, $e$ the energy density, and $S$ the entropy variable. The conjecture asserts that $p$ is a s…

Let $n>0$ and $gamma>0$ denote the particle number density and inverse temperature, respectively, and let $k_B,e,m,c,h$ be the Boltzmann constant, elementary charge, particle mass,…

Let $(\rho_*,v_*)(r)$ be a steady shock for the relativistic Euler equations on the Schwarzschild exterior $r>2M$, and let … where $(\delta_\rho,\delta_v)$ is a compactly supported…

Let $(\rho_*,v_*)=(\rho_*,v_*)(r)$ be a smooth steady state for the relativistic Euler equations on the Schwarzschild exterior $r>2M$. Let … where $(\delta_\rho,\delta_v)$ has comp…

Let $M>0$, let $v=v(t,r)\in[-1,1]$ solve the relativistic Burgers equation on the Schwarzschild exterior $r>2M$, and let the initial data be a compactly perturbed steady shock. Asy…

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

Kinetic equation of state auto-diffeomorphism conjecture. The map $(n,\beta)\leftrightarrow(\eta,\rho)$ given implicitly by these equations is an auto-diffeomorphism of…