Details
| Original language | English |
|---|---|
| Pages (from-to) | 75-91 |
| Number of pages | 17 |
| Journal | Mathematische Zeitschrift |
| Volume | 233 |
| Issue number | 1 |
| Publication status | Published - Jan 2000 |
| Externally published | Yes |
Abstract
We consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution remains bounded but its slope becomes unbounded in finite time. A quite detailed description of the wave-breaking phenomenon is given: there is at least a point (in general depending on time) where the slope becomes infinite exactly at breaking time. The precise blow-up rate is established and for a large class of initial data we also determine the blow-up set.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Zeitschrift, Vol. 233, No. 1, 01.2000, p. 75-91.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
AU - Constantin, Adrian
AU - Escher, Joachim
PY - 2000/1
Y1 - 2000/1
N2 - We consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution remains bounded but its slope becomes unbounded in finite time. A quite detailed description of the wave-breaking phenomenon is given: there is at least a point (in general depending on time) where the slope becomes infinite exactly at breaking time. The precise blow-up rate is established and for a large class of initial data we also determine the blow-up set.
AB - We consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution remains bounded but its slope becomes unbounded in finite time. A quite detailed description of the wave-breaking phenomenon is given: there is at least a point (in general depending on time) where the slope becomes infinite exactly at breaking time. The precise blow-up rate is established and for a large class of initial data we also determine the blow-up set.
UR - http://www.scopus.com/inward/record.url?scp=0034347295&partnerID=8YFLogxK
U2 - 10.1007/PL00004793
DO - 10.1007/PL00004793
M3 - Article
AN - SCOPUS:0034347295
VL - 233
SP - 75
EP - 91
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 1
ER -