Low-regularity Schrödinger maps, II: Global well-posedness in dimensions d 3

Alexandru D. Ionescu; Carlos E. Kenig

doi:10.1007/s00220-006-0180-4

Low-regularity Schrödinger maps, II: Global well-posedness in dimensions d 3

Alexandru D. Ionescu, Carlos E. Kenig

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

50 Scopus citations

Abstract

In dimensions d ≥3, we prove that the Schrödinger map initial-value problem ∂ _tS=s× Δ_x s on ℝ^d× ℝ; s(0)=s₀ is globally well-posed for small data s ₀ in the critical Besov spaces B_t ^d/2 (ℝ; double script S sign²), Q ε double script S sign₂.

Original language	English (US)
Pages (from-to)	523-559
Number of pages	37
Journal	Communications In Mathematical Physics
Volume	271
Issue number	2
DOIs	https://doi.org/10.1007/s00220-006-0180-4
State	Published - Apr 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s00220-006-0180-4

Cite this

@article{fee3682e5f6d48118a83d6798ed69d74,

title = "Low-regularity Schr{\"o}dinger maps, II: Global well-posedness in dimensions d 3",

abstract = "In dimensions d ≥3, we prove that the Schr{\"o}dinger map initial-value problem ∂ tS=s× Δx s on ℝd× ℝ; s(0)=s0 is globally well-posed for small data s 0 in the critical Besov spaces Bt d/2 (ℝ; double script S sign2), Q ε double script S sign2.",

author = "Ionescu, {Alexandru D.} and Kenig, {Carlos E.}",

year = "2007",

month = apr,

doi = "10.1007/s00220-006-0180-4",

language = "English (US)",

volume = "271",

pages = "523--559",

journal = "Communications In Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Low-regularity Schrödinger maps, II

T2 - Global well-posedness in dimensions d 3

AU - Ionescu, Alexandru D.

AU - Kenig, Carlos E.

PY - 2007/4

Y1 - 2007/4

N2 - In dimensions d ≥3, we prove that the Schrödinger map initial-value problem ∂ tS=s× Δx s on ℝd× ℝ; s(0)=s0 is globally well-posed for small data s 0 in the critical Besov spaces Bt d/2 (ℝ; double script S sign2), Q ε double script S sign2.

AB - In dimensions d ≥3, we prove that the Schrödinger map initial-value problem ∂ tS=s× Δx s on ℝd× ℝ; s(0)=s0 is globally well-posed for small data s 0 in the critical Besov spaces Bt d/2 (ℝ; double script S sign2), Q ε double script S sign2.

UR - http://www.scopus.com/inward/record.url?scp=33847632512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847632512&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-0180-4

DO - 10.1007/s00220-006-0180-4

M3 - Article

AN - SCOPUS:33847632512

SN - 0010-3616

VL - 271

SP - 523

EP - 559

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -

Low-regularity Schrödinger maps, II: Global well-posedness in dimensions d 3

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this