Complex valued semi-linear heat equations in super-critical spaces $E_{\sigma }^s$

Jie Chen, Baoxiang Wang, Zimeng Wang

We consider the Cauchy problem for the complex valued semi-linear heat equation $${\partial }_{t}u-\Delta u-u^m=0,u(0,x)=u_0(x),$$ where $m\ge 2$ is an integer and the initia…