Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $ L_{l o c}^{2}\left(\right.R^{3}\left.\right) $

Dongho Chae; Jörg Wolf

doi:10.1016/j.anihpc.2017.10.001

JournalsaihpcVol. 35, No. 4pp. 1019–1039

Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $L_{l oc}^{2} (R^{3})$

Dongho Chae
Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea
Jörg Wolf
Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

$Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $ L_{l o c}^{2}\left(\right.R^{3}\left.\right) $ cover$

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Abstract

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 $L_{l oc}^{2} (R^{3})$ .

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Dongho Chae, Jörg Wolf, Existence of discretely self-similar solutions to the Navier–Stokes equations for initial value in $L_{l oc}^{2} (R^{3})$ . Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 4, pp. 1019–1039

DOI 10.1016/J.ANIHPC.2017.10.001