La ecuación de Navier-Stokes y multifractales
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| Autor: | |
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| Formato: | artículo original |
| Estado: | Versión publicada |
| Fecha de Publicación: | 2008 |
| Descripción: | There is currently no general theorem on the existence and unicity of solutions to the Navier-Stokes equation, which describes the flow of a viscous and incompressible fluid. This is an open problem at the international level, known as the millennium prize problem, for which the Clay Institute of France is offering one million dollars since may 2000.The purpose of this article is to present a brief revision of the most important aspects of the evolution and current status of the problem. Our contribution is the analytical description of turbulence, fully developed, through the resolution rates and the features of multifractal processes, as a collection of generalized Cantor processes. We present four models for the distribution of velocity variations. The first one is based on the life times and risk functions for the interaction between the vortices and their later fragmentation in ever smaller and more numerous vortices. The second one is based on potentiated Bernoulli tests, and we found the number of features, the spectrum, and the structure function. We found the relationship of the shapeparameters with the box dimension of the maximum spectrum as well as with the local dimensions and we described qualitatively the associated tree.The above-mentioned rates serve as support, not only for the description of a three-dimensional model of intermittent turbulence that generalizes the Kolmogorov paradigmatic result, but also for the energy transferred in each stage of the fractalization process, and also for the number of characteristic exponents, which produces a higher level for Hausdorff’s dimension of the set of singularities of the solution. |
| País: | Portal de Revistas UCR |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Lenguaje: | Español |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/288 |
| Acceso en línea: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/288 |
| Palabra clave: | Navier-Stokes turbulence intermittency multifractals velocity gradients turbulencia intermitencia multifractales gradientes de velocidad |