To refer to this page use:
|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.|
|Electronic Publication Date:||20-Feb-2014|
|Citation:||Chae, Dongho, Constantin, Peter, Wu, Jiahong. (2014). An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 16 (473 - 480. doi:10.1007/s00021-014-0166-5|
|Pages:||473 - 480|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||JOURNAL OF MATHEMATICAL FLUID MECHANICS|
Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.