H\"older spaces solvability of a model initial-boundary value problem generated by a problem on a motion of two fluids
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 22, Tome 188 (1991), pp. 5-44
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The initial-boundary value problem for the Stokes system
with discontinuous coefficients of viscosity and density on a
plane $\{x_3=0\}$ is considered. This model problem is given rise
by a problem on an unsteady motion of two fluids separated by
a free surface. We take into account a surface tension which
enters in the boundary conditions for a jump of normal stresses
on the plane $\{x_3=0\}$ аs а non-coercetiv term containing the
integral with respect to time.
The existence of unique solution of this problem is proved
in Hölder spaces. The proof of the solvability and Hölder estimates
of the solution is based on modifications of a theorem of
the Fourier multipliers.
@article{ZNSL_1991_188_a0,
author = {I. V. Denisova and V. A. Solonnikov},
title = {H\"older spaces solvability of a model initial-boundary value problem generated by a problem on a motion of two fluids},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--44},
publisher = {mathdoc},
volume = {188},
year = {1991},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a0/}
}
TY - JOUR AU - I. V. Denisova AU - V. A. Solonnikov TI - H\"older spaces solvability of a model initial-boundary value problem generated by a problem on a motion of two fluids JO - Zapiski Nauchnykh Seminarov POMI PY - 1991 SP - 5 EP - 44 VL - 188 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a0/ LA - ru ID - ZNSL_1991_188_a0 ER -
%0 Journal Article %A I. V. Denisova %A V. A. Solonnikov %T H\"older spaces solvability of a model initial-boundary value problem generated by a problem on a motion of two fluids %J Zapiski Nauchnykh Seminarov POMI %D 1991 %P 5-44 %V 188 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a0/ %G ru %F ZNSL_1991_188_a0
I. V. Denisova; V. A. Solonnikov. H\"older spaces solvability of a model initial-boundary value problem generated by a problem on a motion of two fluids. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 22, Tome 188 (1991), pp. 5-44. http://geodesic.mathdoc.fr/item/ZNSL_1991_188_a0/