Unconditional small data global well-posedness for nonlinear beam equations with weak damping

In this paper, we investigate the large time behavior of a global solution for the nonlinear beam equation with a weak damping term in weighted Sobolev spaces. We proved the unconditional global well-posedness for small initial data and sharp decay estimates of the global solution in the same framework. The crucial part of our proof is a smoothing effect from the linear principal part to overcome the regularity loss structure in the weighted estimates.