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Blow-up phenomena, ill-posedness and peakon solutions for the periodic Euler-Poincaré equations.
- Source :
-
Journal of Differential Equations . Feb2020, Vol. 268 Issue 4, p1307-1325. 19p. - Publication Year :
- 2020
-
Abstract
- In this paper we mainly investigate the initial value problem of the periodic Euler-Poincaré equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant properties of the system. Then, we prove that the periodic Euler-Poincaré equations are ill-posed in critical Besov spaces by a contradiction argument. Finally, we verify the system possesses a class of peakon solutions in the sense of distributions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 268
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 140316098
- Full Text :
- https://doi.org/10.1016/j.jde.2019.08.042