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

Abstract

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.