Smoothing effect for some Schrödinger equations

Nakao Hayashi, Tohru Ozawa

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

We study the Cauchy problem for the following Schrödinger equation in Rn(n∈N): i∂tu + 1 2Δu = V1u + (V2 * |u|2)u, (t,x)∈R×Rn, u(0) = φ, x∈Rn, (**) where V1 = V1(x) = λ1 |x|-γ1, V2 = V2(x) = ∑k = 23 λk |x|-γk, λk∈R (1 ≤ k ≤ 3), 0 < γ1 < min(2, n 2), 0 < γ2, γ3 < min(2, n). We prove the existence, uniqueness, and smoothing effect of global solutions of (**) with φ not necessarily in the Sobolev space H1(Rn).

Original languageEnglish
Pages (from-to)307-348
Number of pages42
JournalJournal of Functional Analysis
Volume85
Issue number2
DOIs
Publication statusPublished - 1989 Aug
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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