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We investigate the global existence and scattering for the cubic fourth‐order Schrödinger equation    i   u  t   +   Δ  2   u  +    |  u  |   2   u  =  0    in a low regularity spaceH  s    (    R   n   )with    s  <  2   . We provide an alternative approach to obtain a new interaction Morawetz estimate which extends the range of the dimension of the interaction Morawetz estimate in Pausader [29][B. Pausader, 2009]. We utilize the interaction Morawetz estimates and the I‐method to prove the global well‐posed and scattering result.

Scattering theory below energy for the cubic fourth‐order Schrödinger equation