Published November 2010
| Version v1
Journal article
Singularity formations for a surface wave model
- 1. Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid (Spain)
- 2. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637 (United States)
Description
In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303–36; Marsden and Weinstein 1983 Physica D 7 305–23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown
Availability note (English)
Available from http://dx.doi.org/10.1088/0951-7715/23/11/006Additional details
Identifiers
- DOI
- 10.1088/0951-7715/23/11/006;
- PII
- S0951-7715(10)59006-6;
Publishing Information
- Journal Title
- Nonlinearity (Print)
- Journal Volume
- 23
- Journal Issue
- 11
- Journal Page Range
- p. 2835-2847
- ISSN
- 0951-7715
INIS
- Country of Publication
- United Kingdom
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 45034500
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- APPROXIMATIONS; HILBERT TRANSFORMATION; MATHEMATICAL MODELS; SINGULARITY; VORTICES; WAVE PROPAGATION
- Descriptors DEC
- CALCULATION METHODS; INTEGRAL TRANSFORMATIONS; TRANSFORMATIONS