Soliton resolution for the energy-critical nonlinear Ginzburg-Landau equation in the radial case

Abstract

We study the the energy critical non-linear Ginzburg-Landau equation $\partial_{t} u =z\Delta u+z|u|^{\frac{4}{D-2}} u$ with $\Re z >0$ in dimension $D\geq 3$. We prove that every radial solution with finite energy norm resolves into a finite superposition of asymptotically decoupled copies of the ground state and free radiation continuously in time.