3 problems

Let $g$ be a power-law interaction kernel with exponent $\alpha$ in dimension $N$, and consider the discrete energies … and the continuum energy … For minimizers…

Carrillo–Huang conjecture. These steady-state solutions should be the unique global minimizers of the associated interaction energy.

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…