Global H1H1 solvability of the 3D logarithmic Schrödinger equation

In this paper we investigate the existence of a unique global mild solution in H1(R3)H1(R3) of the initial-boundary value problem associated with the logarithmic Schrödinger equation i∂tψ=−DΔψ+σlog(|ψ|2)ψ, with D>0D>0 and σ∈R∖{0}σ∈R∖{0}.