| dc.contributor.author | Fanelli, Francesco | |
| dc.contributor.author | Granero Belinchón, Rafael | |
| dc.contributor.other | Universidad de Cantabria | es_ES |
| dc.date.accessioned | 2023-08-04T16:20:05Z | |
| dc.date.available | 2023-08-04T16:20:05Z | |
| dc.date.issued | 2022-07-25 | |
| dc.identifier.issn | 0044-2275 | |
| dc.identifier.issn | 1420-9039 | |
| dc.identifier.other | PID2019-109348GA-I00 | es_ES |
| dc.identifier.uri | https://hdl.handle.net/10902/29604 | |
| dc.description.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 | es_ES |
| dc.description.sponsorship | The authors are very grateful to the anonymous referees for their careful reading and constructive remarks, as well as for pointing out several interesting references related to the present work. The work of both authors has been partially supported by the project “TURB1D—Reduced models of turbulence”, operated by the French CNRS through the program “International Emerging Actions 2019”. The work of the first author has been partially supported by the LABEX MILYON (ANR-10-LABX-0070) of Universit´e de Lyon, within the program “Investissement d’Avenir” (ANR-11-IDEX-0007), and by the projects BORDS (ANR-16-CE40-0027-01), SingFlows (ANR-18-CE40-0027) and CRISIS (ANR-20-CE40-0020-01), all operated by the French National Research Agency (ANR). The work of the second author was supported by the project “Mathematical Analysis of Fluids and Applications” Grant PID2019-109348GA-I00 funded by MCIN/AEI/ 10.13039/501100011033 and acronym “MAFyA”. This publication is part of the project PID2019-109348GA-I00 funded by MCIN/ AEI /10.13039/501100011033. This publication is also supported by a 2021 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. The BBVA Foundation accepts no responsibility for the opinions, statements and contents included in the project and/or the results thereof, which are entirely the responsibility of the authors. | es_ES |
| dc.format.extent | 20 p. | es_ES |
| dc.language.iso | eng | es_ES |
| dc.publisher | Springer | es_ES |
| dc.rights | This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00033-022-01818-5 | es_ES |
| dc.source | Zeitschrift fur Angewandte Mathematik und Physik, 2022, 73, 180 | es_ES |
| dc.subject.other | Nonlinear Parabolic Systems | es_ES |
| dc.subject.other | Degeneracy | es_ES |
| dc.subject.other | Local Well-Posedness | es_ES |
| dc.subject.other | Finite Time Blow-Up | es_ES |
| dc.subject.other | Curvature | es_ES |
| dc.subject.other | Turbulence | es_ES |
| dc.title | Finite time blow-up for some parabolic systems arising in turbulence theory | es_ES |
| dc.type | info:eu-repo/semantics/article | es_ES |
| dc.relation.publisherVersion | https://doi.org/10.1007/s00033-022-01818-5 | es_ES |
| dc.rights.accessRights | openAccess | es_ES |
| dc.identifier.DOI | 10.1007/s00033-022-01818-5 | |
| dc.type.version | acceptedVersion | es_ES |
