Details
| Original language | English |
|---|---|
| Pages (from-to) | 51-80 |
| Number of pages | 30 |
| Journal | Journal für die reine und angewandte Mathematik |
| Issue number | 624 |
| Publication status | Published - 1 Nov 2008 |
Abstract
In the paper we first establish the local well-posedness for a family of nonlinear dispersive equations, the so called b-equation. Then we describe the precise blow-up scenario. Moreover, we prove that for the b-equation we do have the coexistence of global in time solutions and blow-up phenomena: Depending on the initial data solutions may exist for ever, while other data force the solution to produce a singularity in finite time. Finally, we prove the uniqueness and existence of global weak solution to the equation provided the initial data satisfy certain sign conditions.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal für die reine und angewandte Mathematik, No. 624, 01.11.2008, p. 51-80.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-posedness, blow-up phenomena, and global solutions for the b-equation
AU - Escher, Joachim
AU - Yin, Zhaoyang
N1 - Funding information: Acknowledgments. Yin was partially supported by the Alexander von Humboldt Foundation, the NNSF of China (No. 10531040), the SRF for ROCS, SEM, and the NSF of Guangdong Province. The authors thank the referee for valuable comments and suggestions, in particular for pointing out the reference [35].
PY - 2008/11/1
Y1 - 2008/11/1
N2 - In the paper we first establish the local well-posedness for a family of nonlinear dispersive equations, the so called b-equation. Then we describe the precise blow-up scenario. Moreover, we prove that for the b-equation we do have the coexistence of global in time solutions and blow-up phenomena: Depending on the initial data solutions may exist for ever, while other data force the solution to produce a singularity in finite time. Finally, we prove the uniqueness and existence of global weak solution to the equation provided the initial data satisfy certain sign conditions.
AB - In the paper we first establish the local well-posedness for a family of nonlinear dispersive equations, the so called b-equation. Then we describe the precise blow-up scenario. Moreover, we prove that for the b-equation we do have the coexistence of global in time solutions and blow-up phenomena: Depending on the initial data solutions may exist for ever, while other data force the solution to produce a singularity in finite time. Finally, we prove the uniqueness and existence of global weak solution to the equation provided the initial data satisfy certain sign conditions.
UR - http://www.scopus.com/inward/record.url?scp=55249108067&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2008.080
DO - 10.1515/CRELLE.2008.080
M3 - Article
AN - SCOPUS:55249108067
SP - 51
EP - 80
JO - Journal für die reine und angewandte Mathematik
JF - Journal für die reine und angewandte Mathematik
SN - 0075-4102
IS - 624
ER -