Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations TeX Export

@misc{citeulike:532448, abstract = {We prove the nonexistence of local self-similar solutions of the three dimensional incompressible Navier-Stokes equations. The local self-similar solutions we consider here are different from the global self-similar solutions. The self-similar scaling is only valid in an inner core region which shrinks to a point dynamically as the time, \$t\$, approaches the singularity time, \$T\$. The solution outside the inner core region is assumed to be regular. Under the assumption that the local self-similar velocity profile converges to a limiting profile as \$t \to T\$ in \$L^p\$ for some \$p \in (3,\infty)\$, we prove that such local self-similar blow-up is not possible for any finite time.}, archivePrefix = {arXiv}, author = {Hou, Thomas Y. and Li, Ruo}, citeulike-article-id = {532448}, citeulike-linkout-0 = {http://arxiv.org/abs/math.AP/0603126}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.AP/0603126}, day = {6}, eprint = {math.AP/0603126}, keywords = {3d, blow-up, navier-stokes, turbulence}, month = {Mar}, posted-at = {2006-03-07 13:14:12}, priority = {2}, title = {Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations}, url = {http://arxiv.org/abs/math.AP/0603126}, year = {2006} }

TY - ELEC ID - citeulike:532448 L3 - citeulike-article-id:532448 N2 - We prove the nonexistence of local self-similar solutions of the three dimensional incompressible Navier-Stokes equations. The local self-similar solutions we consider here are different from the global self-similar solutions. The self-similar scaling is only valid in an inner core region which shrinks to a point dynamically as the time, $t$, approaches the singularity time, $T$. The solution outside the inner core region is assumed to be regular. Under the assumption that the local self-similar velocity profile converges to a limiting profile as $t \to T$ in $L^p$ for some $p \in (3,\infty)$, we prove that such local self-similar blow-up is not possible for any finite time. TI - Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations KW - 3d KW - blow-up KW - navier-stokes KW - turbulence AU - Hou, Thomas AU - Li, Ruo PY - 2006/Mar/06/ UR - http://arxiv.org/abs/math.AP/0603126 ER -