<p style='text-indent:20px;'>In this paper, we study the nonlinear Schrödinger equation with a partial confinement. By applying the cross-constrained variational arguments and invariant manifolds of the evolution flow, the sharp condition for global existence and blowup of the solution is derived.</p>

中文翻译：

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具有部分约束的交叉约束变分法和非线性薛定谔方程

<p style='text-indent:20px;'>在本文中，我们研究了具有部分约束的非线性薛定谔方程。通过应用演化流的交叉约束变分参数和不变流形，推导出解的全局存在和爆炸的尖锐条件。</p>