Article
Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations
Author/s | Gutiérrez Santacreu, Juan Vicente
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Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2018 |
Deposit Date | 2019-10-22 |
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Abstract | In this paper we construct two families of initial data being arbitrarily large under any
scaling-invariant norm for which their corresponding weak solution to the three-dimensional Navier-
Stokes equations become smooth ... In this paper we construct two families of initial data being arbitrarily large under any scaling-invariant norm for which their corresponding weak solution to the three-dimensional Navier- Stokes equations become smooth on either [0, T1] or [T2,1), respectively, where T1 and T2 are two times prescribed previously. In particular, T1 can be arbitrarily large and T2 can be arbitrarily small. Therefore, possible formation of singularities would occur after a very long or short evolution time, respectively. We further prove that if a large part of the kinetic energy is consumed prior to the first (possible) blow-up time, then the global-in-time smoothness of the solutions follows for the two families of initial data. |
Project ID. | MTM2015-69875-P
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Citation | Gutiérrez Santacreu, J.V. (2018). Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations. ArXiv.org, arXiv:1508.04161 |
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