On two-dimensional initial-boundary value problem for the Navier--Stokes equations with discontinuous boundary data
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 159-178
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We consider initial-boundary value problem for the Navier–Stokes equations with boundary conditions $\overrightarrow{v}\bigm|_{x\in\partial\Omega}=\overrightarrow{a}$ assuming that $\overrightarrow{a}$ may have jump discontinuities at a finite number of points $\xi_1,\dots,\xi_m$ of the boundary $\partial\Omega$ of a bounded domain $\Omega\subset\mathbb{R}^2$. It is proved that this problem possesses a unique generalized solution in a finite time interval or for small initial and boundary data. The solution is found in a certain class of vector fields with an infinite energy integral. The case of moving boundary is also considered.
@article{ZNSL_1992_197_a6,
author = {V. A. Solonnikov},
title = {On two-dimensional initial-boundary value problem for the {Navier--Stokes} equations with discontinuous boundary data},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {159--178},
publisher = {mathdoc},
volume = {197},
year = {1992},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a6/}
}
TY - JOUR AU - V. A. Solonnikov TI - On two-dimensional initial-boundary value problem for the Navier--Stokes equations with discontinuous boundary data JO - Zapiski Nauchnykh Seminarov POMI PY - 1992 SP - 159 EP - 178 VL - 197 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a6/ LA - ru ID - ZNSL_1992_197_a6 ER -
%0 Journal Article %A V. A. Solonnikov %T On two-dimensional initial-boundary value problem for the Navier--Stokes equations with discontinuous boundary data %J Zapiski Nauchnykh Seminarov POMI %D 1992 %P 159-178 %V 197 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a6/ %G ru %F ZNSL_1992_197_a6
V. A. Solonnikov. On two-dimensional initial-boundary value problem for the Navier--Stokes equations with discontinuous boundary data. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 159-178. http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a6/