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Finite time blow-up for some parabolic systems arising in turbulence theory

Abstract: We study a class of nonlinear parabolic systems relevant in turbulence theory. Those systems can be viewed as simplified versions of the Prandtl one-equation and Kolmogorov two-equation models of turbulence. We restrict our attention to the case of one space dimension. We consider initial data for which the diffusion coefficients may vanish. We prove that, under this condition, those systems are locally well-posed in the class of Sobolev spaces of high enough regularity, but also that there exist smooth initial data for which the corresponding solutions blow up in finite time. We are able to put in evidence two different types of blow-up mechanism. In addition, the results are extended to the case of transport-diffusion systems, namely to the case when convection is taken into account

 Autoría: Fanelli F., Granero-Belinchón R.,

 Fuente: Zeitschrift fur Angewandte Mathematik und Physik, 2022, 73, 180

 Editorial: Springer

 Fecha de publicación: 25/07/2022

 Nº de páginas: 19

 Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00033-022-01818-5

 ISSN: 0044-2275,1420-9039

 Proyecto español: PID2019-109348GA-I00

 Url de la publicación: https://doi.org/10.1007/s00033-022-01818-5

Autoría

FANELLI, FRANCESCO