Abstract
We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation in the super critical case i∂tu+14∂x4u=λ∂x(|u|ρ−1u), where ρ>4, λ∈C. We prove the global existence and the large time asymptotics of solutions for small initial data u0∈H1∩H12,1, when the order of the nonlinearity ρ>4.
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