Physics – Fluid Dynamics
Scientific paper
2006-06-14
Physica D: Nonlinear Phenomena, Volume 217, Issue 1, 1 May 2006, Pages 58-63
Physics
Fluid Dynamics
Scientific paper
10.1016/j.physd.2006.03.005
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from a physical point of view, since they imply the connection among the macroscopic and the microscopic scale. Therefore, the appearence of this type of singularity or a similar one might be interpreted as a possible explanation of the transition to turbulence. In order to clarify the question, some one-dimensional models for ideal incompressible hydrodynamics have been introduced and analyzed, and it was proven that shock-waves appear in finite time within this type of flow. In this work we question the validity of these models and analyze the physical meaning that the occurrence of a singularity in an incompressible flow, if it happens, may have.
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