8 problems

Let $A$ be the aggregate potential parameter for a Quasi-Morse potential, and let a flock profile mean a stationary spatial configuration of the corresponding aggregation model. Ca…

Let $\rho(t)$ be the solution on the one-dimensional torus $\mathbb T$, and let $T$ denote a possible singularity time. The numerical simulations consider the convex mobility…

Consider the aggregation model studied in the paper, with exponent $m>2$, and let the equilibria be those studied in Sections 5 and 6. Global-attractor conjecture. These equilibria…

Non-confinement conjecture. For the continuum system, the support of the density should become unbounded over time; equivalently, the confinement result should not hold for the H-s…

Consider the interaction equation as the gradient flow of an interaction energy in the space of Borel probability measures with finite second moment, with interaction potential sat…

Radial blowup profile conjecture. This class of radially symmetric decreasing solutions, including a Dirac mass at the origin, describes well the local behavior at the blowup time…

Global-attractor conjecture. Based on numerical experiments, these equilibria are global attractors for solutions of the aggregation model.

Let $K(x)=|x|^\alpha$ with $0<\alpha<2$, and let the initial data belong to $L_p$ for $p<p_s$. In the special case $\alpha=1$, instantaneous mass concentration has been established…