In this work, we are interested on the study of the Fujita exponent and the meaning of the blow-up for the Fractional Cauchy problem with the Hardy potential, namely, \begin{ equation*} u_t+(-\Delta)^s u=\lambda\dfrac{ u}{ |x|^{ 2s}}+u^{ p}\inn\ren,\\ u(x,0)=u_{ 0}(x)\inn\ren, \end{ equation*} where $N> 2s$, $0<s<1$, $(-\Delta)^s$ is the fractional laplacian of order $2s$, $\l>0$, $u_0\ge 0$, and $1<p<p_{ +}(s,\lambda)$, where $p_{ +}(\lambda, s)$ is the critical existence power found in \cite{ BMP} and \cite{ AMPP}.
Categories: math.AP