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We study the global well-posedness of the two-dimensional defocusingfourth-order Schr\"odinger initial value problem with power type nonlinearities$\vert u\vert^{2k}u$ where $k$ is a positive integer. By using the $I$-method,we prove that global well-posedness is satisfied in the Sobolev spaces$H^{s}(\mathbb{R}^{2})$ for $2-\frac{3}{4k}<s<2$.

Global Well-posedness for The Fourth-order Nonlinear Schr\"{o}dinger Equations on $\mathbb{R}^{2}$