Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2010-2053 |
| Seitenumfang | 44 |
| Fachzeitschrift | Journal of Differential Equations |
| Jahrgang | 258 |
| Ausgabenummer | 6 |
| Publikationsstatus | Veröffentlicht - 15 März 2015 |
Abstract
Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-diffeomorphism of Rd and on its Sobolev completions Dq(Rd). It is shown that the Hs-Sobolev metric induces a strong and smooth Riemannian metric on the Banach manifolds Ds(Rd) for s>1+d2. As a consequence a global well-posedness result of the corresponding geodesic equations, both on the Banach manifold Ds(Rd) and on the smooth regular Fréchet-Lie group of all H∞-diffeomorphisms is obtained. In addition a local existence result for the geodesic equation for metrics of order 12≤s<1+d/2 is derived.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of Differential Equations, Jahrgang 258, Nr. 6, 15.03.2015, S. 2010-2053.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Local and global well-posedness of the fractional order EPDiff equation on Rd
AU - Bauer, Martin
AU - Escher, Joachim
AU - Kolev, Boris
N1 - Funding information: The authors are grateful to Elmar Schrohe and Jörg Seiler for helpful discussions about various topics on translation invariant operators. It is also a pleasure to thank David Lannes for stimulating discussions concerning commutator estimates. Martin Bauer was supported by Austrian Science Fund ( FWF ) project P24625 .
PY - 2015/3/15
Y1 - 2015/3/15
N2 - Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-diffeomorphism of Rd and on its Sobolev completions Dq(Rd). It is shown that the Hs-Sobolev metric induces a strong and smooth Riemannian metric on the Banach manifolds Ds(Rd) for s>1+d2. As a consequence a global well-posedness result of the corresponding geodesic equations, both on the Banach manifold Ds(Rd) and on the smooth regular Fréchet-Lie group of all H∞-diffeomorphisms is obtained. In addition a local existence result for the geodesic equation for metrics of order 12≤s<1+d/2 is derived.
AB - Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-diffeomorphism of Rd and on its Sobolev completions Dq(Rd). It is shown that the Hs-Sobolev metric induces a strong and smooth Riemannian metric on the Banach manifolds Ds(Rd) for s>1+d2. As a consequence a global well-posedness result of the corresponding geodesic equations, both on the Banach manifold Ds(Rd) and on the smooth regular Fréchet-Lie group of all H∞-diffeomorphisms is obtained. In addition a local existence result for the geodesic equation for metrics of order 12≤s<1+d/2 is derived.
KW - Diffeomorphism groups
KW - EPDiff equation
KW - Sobolev metrics of fractional order
UR - http://www.scopus.com/inward/record.url?scp=84921604042&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2014.11.021
DO - 10.1016/j.jde.2014.11.021
M3 - Article
AN - SCOPUS:84921604042
VL - 258
SP - 2010
EP - 2053
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 6
ER -