# American Institute of Mathematical Sciences

doi: 10.3934/mcrf.2021036
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## Cross-constrained variational method and nonlinear Schrödinger equation with partial confinement

 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

* Corresponding author: Jian Zhang

Received  December 2020 Revised  April 2021 Early access July 2021

Fund Project: The project is supported by the National Natural Science Foundation of China (Grant No. 11871138)

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.

Citation: Chenglin Wang, Jian Zhang. Cross-constrained variational method and nonlinear Schrödinger equation with partial confinement. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021036
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