Abstract
We construct a local theory of the Cauchy problem for the nonlinear Schrödinger equations with α ∈ (1, 5) and u 0 ∈ L{frown} p(ℝ) when p lies in an open neighborhood of 2. Moreover we prove the global existence for the initial value problem when p is sufficiently close to 2.
Original language | English |
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Pages (from-to) | 3905-3920 |
Number of pages | 16 |
Journal | Proceedings of the American Mathematical Society |
Volume | 140 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2012 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics