Global existence and uniqueness of Schrödinger maps in dimensions d ≥ 4

I. Bejenaru; A. D. Ionescu; C. E. Kenig

doi:10.1016/j.aim.2007.04.009

Global existence and uniqueness of Schrödinger maps in dimensions d ≥ 4

I. Bejenaru, A. D. Ionescu, C. E. Kenig

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

In dimensions d ≥ 4, we prove that the Schrödinger map initial-value problem{(∂_t s = s × Δ s on R^d × R ;; s (0) = s₀) admits a unique solution s : R^d × R → S² {right arrow, hooked} R³, s ∈ C (R : H_Q^∞), provided that s₀ ∈ H_Q^∞ and {norm of matrix} s₀ - Q {norm of matrix}_{over(H, ̇)d / 2} ≪ 1, where Q ∈ S².

Original language	English (US)
Pages (from-to)	263-291
Number of pages	29
Journal	Advances in Mathematics
Volume	215
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2007.04.009
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

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10.1016/j.aim.2007.04.009

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title = "Global existence and uniqueness of Schr{\"o}dinger maps in dimensions d ≥ 4",

abstract = "In dimensions d ≥ 4, we prove that the Schr{\"o}dinger 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.",

keywords = "A priori estimates, Modified Schr{\"o}dinger maps, Orthonormal frames, Schr{\"o}dinger maps",

author = "I. Bejenaru and Ionescu, {A. D.} and Kenig, {C. E.}",

note = "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: bejenaru@math.ucla.edu (I. Bejenaru), ionescu@math.wisc.edu (A.D. Ionescu), cek@math.uchicago.edu (C.E. Kenig).",

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doi = "10.1016/j.aim.2007.04.009",

language = "English (US)",

volume = "215",

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journal = "Advances in Mathematics",

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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: bejenaru@math.ucla.edu (I. Bejenaru), ionescu@math.wisc.edu (A.D. Ionescu), cek@math.uchicago.edu (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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SP - 263

EP - 291

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Global existence and uniqueness of Schrödinger maps in dimensions d ≥ 4

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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