On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D

Vladimir Georgiev, Chunhua Li

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We consider the scattering problem for the nonlinear Schrödinger equation with a potential in two space dimensions. Appropriate resolvent estimates are proved and applied to estimate the operator A(s) appearing in commutator relations. The equivalence between the operators −ΔV [Formula presented] and −Δ [Formula presented] in L2 norm sense for 0≤s<1 is investigated by using free resolvent estimates and Gaussian estimates for the heat kernel of the Schrödinger operator −ΔV. Our main result guarantees the global existence of solutions and time decay of the solutions assuming initial data have small weighted Sobolev norms. Moreover, the global solutions obtained in the main result scatter.

本文言語English
ページ(範囲)208-218
ページ数11
ジャーナルPhysica D: Nonlinear Phenomena
398
DOI
出版ステータスPublished - 2019 11

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 凝縮系物理学
  • 応用数学

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