Well-posedness of the supercritical Lane-Emden heat flow in Morrey spaces

Simon Blatt, Michael Struwe

For any smoothly bounded domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 3$, and any exponent $p>2^{\ast }=2n/(n-2)$ we study the Lane-Emden heat flow $u_t-\Delta u=|u{|}^{p-2}u$ on $\Omega \times ]0,\infty [$ a…