8 problems

Let $(\rho_0(r),u_0=0)$ be a spherically symmetric stationary solution of the Euler–Poisson system, with polytropic exponent $\gamma$ and steady-state density $\rho_0$. The corresp…

Astrophysicists' instability conjecture. Stationary solutions are unstable whenever

The preceding theorem introduces an exceptional set $\mathcal N\subset(0,\infty)$, of cardinal at most $8$, whose exclusion ensures that the local bifurcation curve is not of the f…

Let $(\rho,v)$ be a GSPS to the pressureless Euler–Poisson equation, with $\rho_0$ compactly supported, center of mass $0$, and total momentum $0$. Let $y_L$, $y_R$, and $f$ be the…

The Euler–Poisson system models a compressible inviscid flow coupled to an electric field, while a de Laval nozzle is described by a varying cross-sectional area whose derivative c…

Consider solutions $(\rho,u)$ of the pressureless Euler–Poisson system, where $\rho$ is the density and $u$ is the velocity. A solution undergoes $C^1$ blow-up when its $C^1$ regul…

Let $\rho$ and $u$ denote the density and velocity in the pressureless Euler–Poisson system, respectively, and let $T_\ast$ be the finite blow-up time. A measure-valued solution al…

Consider two ion species with densities and velocities $(n_1,u_1)$ and $(n_2,u_2)$ satisfying the isothermal Euler–Poisson systems … for $i=1,2$, coupled through … Here $u_{i,0}$ d…