Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 37-48
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It is shown that the initial-boundary value problems for
the Stokes equations with the prescription of velocities $\vec{v}$,
stresses, or of the normal component of velocity and tangential
stresses on the boundary can be reduced to initial-boundary value
problems for systems $\vec{v}_t+A\vec{v}=\vec{f}$ where $A$ is a linear
operator containing a npa-local term (the so called singular
Green operator). For solutions; of these problems coercive estimates
in the sobolev space» $W_2^{\ell,\ell/2}$ and the estimate, of
the norm of the resolving operator in $W_2^r$ are given.
@article{ZNSL_1987_163_a3,
author = {Gerd Grubb and V. A. Solonnikov},
title = {Reduction of basic initial-boundary value problems for the {Stokes} equations to initial-boundary value problems for parabolic systems of pseudodifferential equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {37--48},
publisher = {mathdoc},
volume = {163},
year = {1987},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a3/}
}
TY - JOUR AU - Gerd Grubb AU - V. A. Solonnikov TI - Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations JO - Zapiski Nauchnykh Seminarov POMI PY - 1987 SP - 37 EP - 48 VL - 163 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a3/ LA - ru ID - ZNSL_1987_163_a3 ER -
%0 Journal Article %A Gerd Grubb %A V. A. Solonnikov %T Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations %J Zapiski Nauchnykh Seminarov POMI %D 1987 %P 37-48 %V 163 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a3/ %G ru %F ZNSL_1987_163_a3
Gerd Grubb; V. A. Solonnikov. Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 37-48. http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a3/