A reduced Ginzburg–Landau model in ℝn

In this work, we consider a reduced Ginzburg–Landau model in which the magnetic field is neglected. First, we show the well-posedness of weak solutions and strong solutions in a bounded domain Ω⊂Rn. Finally, we prove the well-posedness of smooth solutions when Ω:=Rn (n≥3).