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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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ISSN
1435-5345
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Volume 2008, Issue 624

Issues

Well-posedness, blow-up phenomena, and global solutions for the b-equation

Joachim Escher
  • Institute for Applied Mathematics, Leibniz University of Hannover, 30167 Hannover, Germany. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Zhaoyang Yin
  • Department of Mathematics, Zhongshan University, Xin Gang Xi Road No. 135, Guangzhou 510275, China. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-10-29 | DOI: https://doi.org/10.1515/CRELLE.2008.080

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.

About the article

Received: 2007-03-14

Revised: 2007-07-13

Published Online: 2008-10-29

Published in Print: 2008-11-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2008, Issue 624, Pages 51–80, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.080.

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