An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations
- Authors
- Chae, Dongho; Constantin, Peter; Wu, Jiahong
- Issue Date
- Sep-2014
- Publisher
- SPRINGER BASEL AG
- Keywords
- Inviscid model; singularity; explicit solutions; 2D Boussinesq equations
- Citation
- JOURNAL OF MATHEMATICAL FLUID MECHANICS, v.16, no.3, pp 473 - 480
- Pages
- 8
- Journal Title
- JOURNAL OF MATHEMATICAL FLUID MECHANICS
- Volume
- 16
- Number
- 3
- Start Page
- 473
- End Page
- 480
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/11847
- DOI
- 10.1007/s00021-014-0166-5
- ISSN
- 1422-6928
1422-6952
- Abstract
- We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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