Well-posedness and singularity formation for the Kolmogorov two-equation model of turbulence in 1-D - Institut Camille Jordan Accéder directement au contenu
Article Dans Une Revue Journal of Dynamics and Differential Equations Année : 2023

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

Résumé

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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Dates et versions

hal-03503786 , version 1 (28-12-2021)

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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. Journal of Dynamics and Differential Equations, 2023, ⟨10.1007/s10884-023-10326-7⟩. ⟨hal-03503786⟩
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