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 $D\ge 3$. 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.

26 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2210.14963, arXiv:2405.06005 by other authors