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

@misc{citeulike:456148, abstract = {We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back to label map. 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.}, archivePrefix = {arXiv}, author = {Chae, Dongho}, citeulike-article-id = {456148}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0601060}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0601060}, day = {4}, eprint = {math/0601060}, keywords = {3d, blow-up, euler-equation}, month = {Jan}, posted-at = {2006-01-05 11:06:37}, priority = {2}, title = {Nonexistence of self-similar singularities for the 3D incompressible Euler equations}, url = {http://arxiv.org/abs/math/0601060}, year = {2006} }

TY - ELEC ID - citeulike:456148 L3 - citeulike-article-id:456148 N2 - We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back to label map. 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. TI - Nonexistence of self-similar singularities for the 3D incompressible Euler equations KW - 3d KW - blow-up KW - euler-equation AU - Chae, Dongho PY - 2006/Jan/04/ UR - http://arxiv.org/abs/math/0601060 ER -