The blow-up solutions of the heat equations in \(\mathcal{F} L^1(\mathbb R^N)\) (Q2355437)

The authors claim to use a new technology in the study of blowing up solutions to the Cauchy problem \[ \begin{cases} \partial_tu-\Delta u=u^p,\quad t>0,\, x\in \mathbb R^N,\\ u(0,x)=u_0(x),\quad x\in \mathbb R^N, \end{cases} \] when \(u_0\in \mathcal{F}L^1=\{f\in \mathcal{S}': \|\hat f\|_{L^1}<\infty\}\).