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Zeitschrift für Analysis und ihre Anwendungen


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Volume 8, Issue 4, 1989, pp. 329–347
DOI: 10.4171/ZAA/357

Published online: 1989-08-31

Solvability of a noncoercive initial-boundary value problem for the Stokes system in Hölder classes of functions (the half-space case) (in Russian)

Ilya S. Mogilevskii and Vsevolod A. Solonnikov[1]

(1) Russian Acadademy of Sciences, St. Petersburg, Russian Federation

The initial-boundary value problem for the Stokes system with the surface tension in boundary conditions is considered in the half-space $\mathbb R_+^3 (x_3 > 0)$. This unique solubility of this problem in Hölder spaces is proved. The proof is based on estimates of the solution in $\mathbb R_{\infty} = \{ (x, t): x \in \mathbb R_+^3, t > 0\}. These estimates are obtained by methods of the Fourier multipliers theory.

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Mogilevskii Ilya, Solonnikov Vsevolod: Solvability of a noncoercive initial-boundary value problem for the Stokes system in Hölder classes of functions (the half-space case) (in Russian). Z. Anal. Anwend. 8 (1989), 329-347. doi: 10.4171/ZAA/357