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arXiv:math/0601060 [math.AP]AbstractReferencesReviewsResources

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

Dongho Chae

Published 2006-01-04, updated 2006-01-16Version 2

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.

Comments: This version refines the previous one by relaxing the condition of compact support for the vorticity
Categories: math.AP, math-ph, math.MP
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