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
Russian Acadademy of Sciences, St. Petersburg, Russian FederationVsevolod A. Solonnikov
Russian Acadademy of Sciences, St. Petersburg, Russian Federation
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Abstract
The initial-boundary value problem for the Stokes system with the surface tension in boundary conditions is considered in the half-space . 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.
Cite this article
Ilya S. Mogilevskii, Vsevolod A. Solonnikov, 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), no. 4, pp. 329–347
DOI 10.4171/ZAA/357