TY - JOUR
T1 - Global existence and uniqueness of Schrödinger maps in dimensions d ≥ 4
AU - Bejenaru, I.
AU - Ionescu, A. D.
AU - Kenig, C. E.
N1 - Funding Information:
✩ The second author was supported in part by an NSF grant and a Packard fellowship. The third author was supported in part by an NSF grant. * Corresponding author. E-mail addresses: [email protected] (I. Bejenaru), [email protected] (A.D. Ionescu), [email protected] (C.E. Kenig).
PY - 2007/10/20
Y1 - 2007/10/20
N2 - 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.
AB - 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.
KW - A priori estimates
KW - Modified Schrödinger maps
KW - Orthonormal frames
KW - Schrödinger maps
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U2 - 10.1016/j.aim.2007.04.009
DO - 10.1016/j.aim.2007.04.009
M3 - Article
AN - SCOPUS:34447526310
SN - 0001-8708
VL - 215
SP - 263
EP - 291
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 1
ER -