Fractional heat equation involving Hardy-Leray Potential

In this paper we analyse the existence and non-existence of non-negative solutions to a non-local parabolic equation with a Hardy-Leray type potential. More precisely, we consider the problem cases (wₜ- w) ˢ=|x|^{2s} w+wᵖ +f, & in RN (0, +), \\ w (x, t) =0, & in RN (-, 0], cases where N> 2s, 0p_+ (, s). Then there are not any non-negative supersolutions. - Let p<p_+ (, s). Then there exist local solutions while concerning global solutions we need to distinguish two cases: - Let 1< p F (, s). Here we show that a weighted norm of any positive solution blows up in finite time. - Let F (, s) <p<p_+ (, s). Here we prove the existence of global solutions under suitable hypotheses.