Abstract
In dimensions d ≥ 4, we prove that the Schrödinger map initial-value problem{(∂t s = s × Δ s on Rd × R ;; s (0) = s0) admits a unique solution s : Rd × R → S2 {right arrow, hooked} R3, s ∈ C (R : HQ∞), provided that s0 ∈ HQ∞ and {norm of matrix} s0 - Q {norm of matrix}over(H, ̇)d / 2 ≪ 1, where Q ∈ S2.
Original language | English (US) |
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Pages (from-to) | 263-291 |
Number of pages | 29 |
Journal | Advances in Mathematics |
Volume | 215 |
Issue number | 1 |
DOIs | |
State | Published - Oct 20 2007 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
Keywords
- A priori estimates
- Modified Schrödinger maps
- Orthonormal frames
- Schrödinger maps