Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $ {L}_{loc}^{2}({\mathbb{R}}^{3})$

Chae, Dongho; Wolf, Jörg

doi:10.1016/j.anihpc.2017.10.001

Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in

L_{l o c}^{2} (R^{3})

Chae, Dongho ; Wolf, Jörg

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 1019-1039

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Résumé

We prove the existence of a forward discretely self-similar solutions to the Navier–Stokes equations in $R^{3} \times (0, + \infty)$ for a discretely self-similar initial velocity belonging to $L_{l o c}^{2} (R^{3})$ .

MR Zbl

DOI : 10.1016/j.anihpc.2017.10.001

Classification : 76B03, 35Q31
Keywords: Navier–Stokes equations, Existence, Discretely self-similar solutions

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     author = {Chae, Dongho and Wolf, J\"org},
     title = {Existence of discretely self-similar solutions to the {Navier{\textendash}Stokes} equations for initial value in $ {L}_{loc}^{2}({\mathbb{R}}^{3})$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1019--1039},
     publisher = {Elsevier},
     volume = {35},
     number = {4},
     year = {2018},
     doi = {10.1016/j.anihpc.2017.10.001},
     mrnumber = {3795025},
     zbl = {1391.76057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.10.001/}
}

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Chae, Dongho; Wolf, Jörg. Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $ {L}_{loc}^{2}({\mathbb{R}}^{3})$. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 1019-1039. doi: 10.1016/j.anihpc.2017.10.001

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