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

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

2006-01-04

arxiv.org/abs/math/0601060v2

Mathematics

Analysis of PDEs

This version refines the previous one by relaxing the condition of compact support for the vorticity

Scientific paper

10.1007/s00220-007-0249-8

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.

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