In unbounded domain ${\mathbf{R}}^N,N\ge 1$, we consider the defocusing nonlinear Schrödinger equation with power-type nonlinearity containing $-{\left|u\right|}^{\frac{4}{N-2s}}u$. For $2_s^{\ast }=\frac{2}{N-2s}$, with $s<\frac{N}{2}$ and $s\le 1$, the corresponding scaling invariant space is homogeneous Sobolev ${\dot{H}}_x^s\left({\mathbf{R}}^N\right)$ and in this case implies that the critical regularity is $s_c=\frac{N}{2}-\frac{1}{2_s^{\ast }}\equiv s$. Under the finite variance condition of initial data and the solutions of the problem satisfy the pseudo-conformal conservation law, we investigate the global existence of the solutions in $L_t^q-L_x^p$ spaces for some constants $p,q\ge 2$ depending on $N,s$. The new results of this study encompass the existing results on mass critical $(s_c=0)$ in Dodson (2012) and energy critical $(s_c=1)$ in Killip and Visan (2010).

在无界域中${\mathbf{R}}^{ñ},ñ\ge 1$，我们考虑具有幂型非线性的散焦非线性薛定谔方程包含$-{\left|你\right|}^{\frac{4}{ñ-2s}}你$. 为了$2_s^{*}=\frac{2}{ñ-2s}$， 和$s<\frac{ñ}{2}$和$s\le 1$, 对应的尺度不变空间是齐次 Sobolev${\dot{H}}_X^s\left({\mathbf{R}}^{ñ}\right)$在这种情况下，意味着临界规律是$s_C=\frac{ñ}{2}-\frac{1}{2_s^{*}}\equiv s$. 在初始数据的有限方差条件下，问题的解满足伪共形守恒定律，我们研究了解的全局存在性${\mathrm{大号}}_{吨}^q-{\mathrm{大号}}_X^p$一些常数的空间$p,q\ge 2$根据$ñ,s$. 这项研究的新结果包含了质量关键的现有结果$(s_C=0)$在 Dodson (2012) 和能源关键$(s_C=1)$在 Killip 和 Visan (2010)。