On the deformations of the incompressible Euler equations |
| |
Authors: | Dongho Chae |
| |
Institution: | (1) Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea |
| |
Abstract: | We consider systems of deformed system of equations, which are obtained by some transformations from the system of incompressible
Euler equations. These have similar properties to the original Euler equations including the scaling invariance. For one form
of deformed system we prove that finite time blow-up actually occurs for ‘generic’ initial data, while for the other form
of the deformed system we prove the global in time regularity for smooth initial data. Moreover, using the explicit functional
relations between the solutions of those deformed systems and that of the original Euler system, we derive the condition of
finite time blow-up of the Euler system in terms of solutions of one of its deformed systems. As another application of those
relations we deduce a lower estimate of the possible blow-up time of the 3D Euler equations.
This research was supported partially by the KOSEF Grant no. R01-2005-000-10077-0 |
| |
Keywords: | Euler equations Deformations Blow-up problem |
本文献已被 SpringerLink 等数据库收录! |
|