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The well-posedness for the Camassa-Holm type equations in critical Besov spaces [formula omitted] with 1 ≤ p < +∞.
- Source :
-
Journal of Differential Equations . Sep2023, Vol. 367, p729-748. 20p. - Publication Year :
- 2023
-
Abstract
- For the famous Camassa-Holm equation, the well-posedness in C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p ≤ 2 and the ill-posedness in C ([ 0 , T ] ; B ∞ , 1 1 (R)) had been studied in [15,16,23]. That is to say, it left an open problem in the critical case C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 2 < p < + ∞ proposed by Danchin in [15,16]. In this paper, we solve this problem and obtain the local well-posedness for the Camassa-Holm equation in critical Besov spaces C ([ 0 , T ] ; B p , 1 1 + 1 p (R)) with 1 ≤ p < + ∞. It is worth mentioning that our method is suitable for many Camassa-Holm type equations, such as the Novikov equation and the two-component Camassa-Holm system, and can also improve their index of the local well-posedness. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BESOV spaces
*EQUATIONS
*PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 367
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 164132348
- Full Text :
- https://doi.org/10.1016/j.jde.2023.05.032