Global well-posedness and scattering for the nonstandard defocusing Beam equation

We consider the nonstandard defocusing Beam equation utt+∑i=1n∂i4u+u+|u|p−1u=0 in the subcritical case. We show the global well-posedness and the scattering results in low dimensions by the compactness-rigidity argument of Kenig and Merle (2006, 2008)  [7], [3]. The new ingredient is that we establish the suitable Strichartz estimate to overcome the difficulty caused by the complicated dispersive estimate.