Decay of the stochastic linear Schr\"odinger equation in $d \geq 3$ with small multiplicative noise

@article{Fan2018DecayOT,
  title={Decay of the stochastic linear Schr\"odinger equation in \$d \geq 3\$ with small multiplicative noise},
  author={C. Fan and W. Xu},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
  • C. Fan, W. Xu
  • Published 2018
  • Mathematics
  • arXiv: Analysis of PDEs
  • We give decay estimates of the solution to the linear Schr\"odinger equation in dimension $d \geq 3$ with a small noise which is white in time and colored in space. As a consequence, we also obtain certain asymptotic behaviour of the solution. The proof relies on the bootstrapping argument used by Journ\'e-Soffer-Sogge for decay of deterministic Schr\"odinger operators. 
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