5 problems

For $d>2$, consider nonnegative, nontrivial subsolutions of the Lane–Emden inequality … and let $M_c^{sub}(d)$ be the corresponding minimal mass. Let $M_c(d)$ denote the Keller–Seg…

Let $M_c^{sub}(d)$ denote the minimal mass of nonnegative, nontrivial subsolutions of the Lane–Emden equation … and let $M_c(d)$ be the critical mass of the Keller–Segel system. Cr…

Uniform boundedness conjecture. If $M<8\pi$, then the solutions are uniformly bounded in time.

Let $\rho$to$2\sigma_0$ from below or above, and consider the Dirichlet and Neumann problems on a ball, respectively, with single-peak solutions concentrating at the origin. Here,…

Assume $b1=b2=d=2$ in the generalized Keller–Segel model, and let $M_2$ denote the mass threshold in the finite-time blow-up result for finite second moment, while $M_\gamma$ denot…