Decay estimates for Schrödinger systems with time-dependent potentials in 2D

Shuqi Tang; Chunhua Li; Shuqi Tang; Chunhua Li

doi:10.3934/math.20231002

AIMS Mathematics

2023, Volume 8, Issue 8: 19656-19676. doi: 10.3934/math.20231002

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Research article

Decay estimates for Schrödinger systems with time-dependent potentials in 2D

Shuqi Tang ,
Chunhua Li ^,

Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China

Received: 05 April 2023 Revised: 29 April 2023 Accepted: 08 May 2023 Published: 12 June 2023
MSC : 35B40, 35Q55

We consider the Cauchy problem for systems of nonlinear Schrödinger equations with time-dependent potentials in 2D. Under assumptions about mass resonances and potentials, we prove the global existence of the nonlinear Schrödinger systems with small initial data. In particular, by analyzing the operator $ \Delta $ and time-dependent potentials $ {V_{j}} $ separately, we show that the small global solutions satisfy time decay estimates of order $ O((t\log{t})^{-1}) $ when $ p = 2 $, and the small global solutions satisfy time decay estimates of order $ O({t}^{-1}) $ when $ p > 2 $.
- systems of nonlinear Schrödinger equations,
- time-dependent potentials,
- time decay estimates,
- mass resonances
Citation: Shuqi Tang, Chunhua Li. Decay estimates for Schrödinger systems with time-dependent potentials in 2D[J]. AIMS Mathematics, 2023, 8(8): 19656-19676. doi: 10.3934/math.20231002

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Abstract

We consider the Cauchy problem for systems of nonlinear Schrödinger equations with time-dependent potentials in 2D. Under assumptions about mass resonances and potentials, we prove the global existence of the nonlinear Schrödinger systems with small initial data. In particular, by analyzing the operator $ \Delta $ and time-dependent potentials $ {V_{j}} $ separately, we show that the small global solutions satisfy time decay estimates of order $ O((t\log{t})^{-1}) $ when $ p = 2 $, and the small global solutions satisfy time decay estimates of order $ O({t}^{-1}) $ when $ p > 2 $.

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