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An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations

2014.07.24 17:38

실적년도	2014년
논문구분	국외
총저자	Dongho Chae, Peter Constantin, Jiahong Wu
학술지명	Journal of Mathematical Fluid Mechanics
권(Vol.)
호(No.)
게재년월	년 월
Impact Factor
SCI 등재	SCIE
비고

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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