dorsal/arxiv
View SchemaOn one-dimensional models for hydrodynamics
| Authors | Carlos Escudero |
|---|---|
| Categories | |
| ArXiv ID | physics/0606127 |
| URL | https://arxiv.org/abs/physics/0606127 |
| DOI | 10.1016/j.physd.2006.03.005 |
| Journal | Physica D: Nonlinear Phenomena, Volume 217, Issue 1, 1 May 2006, Pages 58-63 |
Abstract
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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"abstract": "To date it has not been possible to prove whether or not the\nthree-dimensional incompressible Euler equations develop singular behaviour in\nfinite time. Some possible singular scenarios, as for instance shock-waves, are\nvery important from a physical point of view, since they imply the connection\namong the macroscopic and the microscopic scale. Therefore, the appearence of\nthis type of singularity or a similar one might be interpreted as a possible\nexplanation of the transition to turbulence. In order to clarify the question,\nsome one-dimensional models for ideal incompressible hydrodynamics have been\nintroduced and analyzed, and it was proven that shock-waves appear in finite\ntime within this type of flow. In this work we question the validity of these\nmodels and analyze the physical meaning that the occurrence of a singularity in\nan incompressible flow, if it happens, may have.",
"arxiv_id": "physics/0606127",
"authors": [
"Carlos Escudero"
],
"categories": [
"physics.flu-dyn",
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],
"doi": "10.1016/j.physd.2006.03.005",
"journal_ref": "Physica D: Nonlinear Phenomena, Volume 217, Issue 1, 1 May 2006,\n Pages 58-63",
"title": "On one-dimensional models for hydrodynamics",
"url": "https://arxiv.org/abs/physics/0606127"
},
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