Critical norm blow-up for the energy supercritical nonlinear heat equation

Hideyuki Miura, Jin Takahashi

We address the critical norm blow-up problem for the nonlinear heat equation $u_t-\Delta u=|u{|}^{p-1}u$ in ${\mathbf{R}}^n\times (0,T)$. In the supercritical range $p>(n+2)/(n-2)$, we prove…