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Well-posedness and singularity formation for the Kolmogorov two-equation model of turbulence in 1-D

Abstract : We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in Sobolev spaces even in the case of vanishing mean turbulent kinetic energy. Then, we show that, in general, those solutions must blow up in finite time. To the best of our knowledge, these results are the first establishing the well-posedness of the system for vanishing initial data and the occurence of finite time singularities for the model under study.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03503786
Contributor : Francesco Fanelli Connect in order to contact the contributor
Submitted on : Tuesday, December 28, 2021 - 11:56:43 AM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM
Long-term archiving on: : Tuesday, March 29, 2022 - 6:13:47 PM

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F-GB_Kolmogorov.pdf
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  • HAL Id : hal-03503786, version 1
  • ARXIV : 2112.13454

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Francesco Fanelli, Rafael Granero-Belinchón. Well-posedness and singularity formation for the Kolmogorov two-equation model of turbulence in 1-D. 2021. ⟨hal-03503786⟩

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