Weak attractors for the dissipative fractional Heisenberg equation

In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations.

► We study the long time dynamics for the fractional Heisenberg equation. ► Some new commutator structure is introduced to show compactness. ► The existence of a weak attractor is proved.