Critical nonlinear Schrödinger equations in higher space dimensions

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Author(s)

Abstract

<p>We study the critical nonlinear Schrödinger equations \[ i\partial _{t}u+\frac{1}{2}\Delta u = \lambda \vert u\vert^{2/n}u, \quad (t,x) \in \mathbb{R}^{+}\times \mathbb{R}^{n}, \] in space dimensions 𝑛 ≥ 4, where 𝜆 ∈ ℝ. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.</p>

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 70(4), 1475-1492, 2018

    The Mathematical Society of Japan

Codes

  • NII Article ID (NAID)
    130007500591
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • ISSN
    0025-5645
  • NDL Article ID
    029291992
  • NDL Call No.
    Z53-A209
  • Data Source
    NDL  J-STAGE 
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