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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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/
@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},
year = {1987},
volume = {163},
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
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
%U http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a3/
%G ru
%F ZNSL_1987_163_a3
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.
