Energy Solution to a Schrödinger–Poisson System in the Two-Dimensional Whole Space
Energy Solution to a Schrödinger–Poisson System in the Two-Dimensional Whole Space
We consider the Cauchy problem of the two-dimensional Schrödinger–Poisson system in the energy class. Though the Newtonian potential diverges at spatial infinity in the logarithmic order, global well-posedness is proven in both defocusing and focusing cases. The key is a decomposition of the nonlinearity into a sum of the linear …