Asymptotic stability of small solitons for 2D Nonlinear Schrödinger equations with potential
نویسنده
چکیده
We consider asymptotic stability of a small solitary wave to supercritical 2-dimensional nonlinear Schrödinger equations iut +∆u = V u± |u|u for (x, t) ∈ R × R, in the energy class. This problem was studied by Gustafson-NakanishiTsai [14] in the n-dimensional case (n ≥ 3) by using the endpoint Strichartz estimate. Since the endpoint Strichartz estimate fails in 2-dimensional case, we use a time-global local smoothing estimate of Kato type to prove the asymptotic stability of a solitary wave.
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