Details
| Original language | English |
|---|---|
| Pages (from-to) | 449-459 |
| Number of pages | 11 |
| Journal | Monatshefte für Mathematik |
| Volume | 167 |
| Issue number | 3-4 |
| Publication status | Published - 23 Jun 2011 |
Abstract
A geometric approach to the study of natural two-component generalizations of the periodic Hunter-Saxton is presented. We give rigorous evidence of the fact that these systems can be realized as geodesic equations with respect to symmetric linear connections on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle DIFF(S) with the space of smooth functions on the circle. An immediate consequence of this approach is a well-posedness result of the corresponding Cauchy problems in the smooth category.
Keywords
- Euler equation, Geodesic flow, Hunter-Saxton equation, Proudman-Johnson equation, Semidirect product
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Monatshefte für Mathematik, Vol. 167, No. 3-4, 23.06.2011, p. 449-459.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-metric two-component Euler equations on the circle
AU - Escher, Joachim
PY - 2011/6/23
Y1 - 2011/6/23
N2 - A geometric approach to the study of natural two-component generalizations of the periodic Hunter-Saxton is presented. We give rigorous evidence of the fact that these systems can be realized as geodesic equations with respect to symmetric linear connections on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle DIFF(S) with the space of smooth functions on the circle. An immediate consequence of this approach is a well-posedness result of the corresponding Cauchy problems in the smooth category.
AB - A geometric approach to the study of natural two-component generalizations of the periodic Hunter-Saxton is presented. We give rigorous evidence of the fact that these systems can be realized as geodesic equations with respect to symmetric linear connections on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle DIFF(S) with the space of smooth functions on the circle. An immediate consequence of this approach is a well-posedness result of the corresponding Cauchy problems in the smooth category.
KW - Euler equation
KW - Geodesic flow
KW - Hunter-Saxton equation
KW - Proudman-Johnson equation
KW - Semidirect product
UR - http://www.scopus.com/inward/record.url?scp=84865634039&partnerID=8YFLogxK
U2 - 10.1007/s00605-011-0323-3
DO - 10.1007/s00605-011-0323-3
M3 - Article
AN - SCOPUS:84865634039
VL - 167
SP - 449
EP - 459
JO - Monatshefte für Mathematik
JF - Monatshefte für Mathematik
SN - 0026-9255
IS - 3-4
ER -