A Liouville-type theorem for the $3$-dimensional parabolic Gross-Pitaevskii and related systems

Quoc Hung Phan, Philippe Souplet

We prove a Liouville-type theorem for semilinear parabolic systems of the form $${\partial }_t{u}_i-\Delta u_i=\sum _{j=1}^m{\beta }_{ij}{u}_i^r{u}_j^{r+1},i=1,2,...,m$$ in the whole space…