A scaling and energy equality preserving approximation for the 3D Navier-Stokes equations in the finite energy case |
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Authors: | Fré dé ric Leliè vre |
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Affiliation: | Equipe d’Analyse et de Probabilités, Université d’Evry, France |
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Abstract: | We discuss a new model (inspired by the work of Vishik and Fursikov) approximating the 3D Navier-Stokes equations, which preserves the scaling as in the Navier-Stokes equations and thus allows the study of self-similar solutions. Using some energy estimates and Leray’s limiting process, we show the existence of a solution of this model in the finite energy case, and the energy equality and inequality fulfilled by it. This approximation can be shown to converge to the Navier-Stokes equations using a mild approach based on the approximated pressure, and the solution satisfies Scheffer’s local energy inequality, an essential tool for proving Caffarelli, Kohn and Nirenberg’s regularity criterion. We also give a partial result of self-similarity satisfied by the approximated solution in the infinite energy case. |
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Keywords: | 76D05 |
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