Abstract
We study the critical nonlinear Schrödinger equations iδtu +1/2Δu = λ|u|2/nu; (t; x) ∈ R+ × Rn; 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.
Original language | English |
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Pages (from-to) | 1475-1492 |
Number of pages | 18 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 70 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2018 |
Externally published | Yes |
Keywords
- Critical NLS equations
- Higher space dimensions
- Large time asymptotics
ASJC Scopus subject areas
- Mathematics(all)