临界耗散非线性薛定谔方程特殊解的 $L^2$$ - 衰变率

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Annales Henri Poincaré Pub Date : 2023-12-26 DOI:10.1007/s00023-023-01403-0

Takuya Sato

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引用次数: 0

摘要

我们考虑具有临界幂非线性的一维耗散非线性薛定谔方程的考奇问题。在之前的工作中，Ogawa-Sato (Nonlinear Differ Equ Appl 27:18, 2020)展示了耗散解在解析类中的$L^2$-衰减估计值。在本文中，我们通过得到下$L^2$-衰减估计值，证明了前人工作中得到的$L^2$-衰减率对于特殊解是最优的。

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$L^2$-Decay Rate for Special Solutions to Critical Dissipative Nonlinear Schrödinger Equations

We consider the Cauchy problem of one-dimensional dissipative nonlinear Schrödinger equations with a critical power nonlinearity. In the previous work, Ogawa–Sato (Nonlinear Differ Equ Appl 27:18, 2020) showed the upper $L^2$-decay estimate of dissipative solutions in the analytic class. In this paper, we show that $L^2$-decay rate obtained in the previous work is optimal for special solutions by obtaining the lower $L^2$-decay estimate.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.