Abstract
The local well-posedness with small data in Hs(Rn)(s⩾3+max(n/2,1+)) for the Cauchy problem of the fourth order nonlinear Schrödinger equations with the third order derivative nonlinear terms were obtained by Huo and Jia [17]. In this paper we show its global well-posedness with small data in the modulation space M2,17/2 and in Sobolev spaces Hn/2+7+/2. For a special nonlinear term containing only one third order derivative, we can show its global well posedness in M2,11/2 and H(n+1+)/2.
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