On one-dimensional models for hydrodynamics
摘要
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.
引用
@article{arxiv.physics/0606127,
title = {On one-dimensional models for hydrodynamics},
author = {Carlos Escudero},
journal= {arXiv preprint arXiv:physics/0606127},
year = {2009}
}