Abstract
We consider the initial boundary value problem for the Navier-Stokes equations with boundary conditions\(\vec v|\partial \Omega = \vec a\). We assume that\(\vec a\) may have jump discontinuities at finitely many points ξ1;. . .,ξm of the boundary ϖΩ of a bounded domain Ω ⊂ ℝ2. We prove that this problem has a unique generalized solution in a finite time interval or for small initial and boundary data. The solution is found in a class of vector fields with infinite energy integral. The case of a moving boundary is also considered. Bibliography: 11 titles.
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Dedicated to O. A. Ladyzhenskaya on the occasion of her 70th birthday.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 197, pp. 159–178, 1992.
Translated by E. V. Frolova.
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Solonnikov, V.A. On the two-dimensional initial boundary value problem for the Navier-Stokes equations with discontinuous boundary data. J Math Sci 75, 2079–2092 (1995). https://doi.org/10.1007/BF02362947
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DOI: https://doi.org/10.1007/BF02362947