# Critical nonlinear Schrödinger equations in higher space dimensions

## 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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