Cross-constrained variational method and nonlinear Schrödinger equation with partial confinement

Chenglin Wang; Jian Zhang

doi:10.3934/mcrf.2021036

Article Contents

2022, Volume 12, Issue 3: 611-619. Doi: 10.3934/mcrf.2021036

This issue Previous Article A linear quadratic stochastic Stackelberg differential game with time delay Next Article Numerical analysis and simulations of a frictional contact problem with damage and memory

Cross-constrained variational method and nonlinear Schrödinger equation with partial confinement

Chenglin Wang and
Jian Zhang^,

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

^* Corresponding author: Jian Zhang
^* Corresponding author: Jian Zhang

Received: November 30, 2020

Revised: March 31, 2021

Early access: July 2021

Published: July 2022

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55, 35A15; Secondary: 35B30.

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References

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