On nonlinear Schrödinger equations with almost periodic initial data

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Abstract

We consider the Cauchy problem of nonlinear Schrödinger equations (NLS) with almost periodic functions as initial data. We first prove that, given a frequency set ω = {ω_j}_{j=1}^∞, NLS is local well-posed in the algebra A_ω(ℝ) of almost periodic functions with absolutely convergent Fourier series. Then, we prove a finite time blowup result for NLS with a nonlinearity |u|^p, p∈2ℕ. This elementary argument presents the first instance of finite time blowup solutions to NLS with generic almost periodic initial data.
Original languageEnglish
Pages (from-to)1253-1270
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number2
DOIs
Publication statusPublished - 2 Apr 2015

Keywords

  • nonlinear Schrödinger equation
  • well-posedness
  • almost periodic functions
  • finite time blowup solution

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