Abstract
In a class of functions with Holder-continuous derivatives unique solvability is is proved for the problem of determining a solution of the linear, time-dependent system of Navier-Stokes equations with boundary data\(\sum\limits_{j = 1}^s {T_{ij} n_j = 0} \), where are the direction cosines of the exterior normal to the boundary and\(T_{ij} \) are the components of the stress tensor.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 200–218, 1977.
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Solonnikov, V.A. The solvability of the second initial boundary-value problem for the linear, time-dependent system of Navier-Stokes equations. J Math Sci 10, 141–155 (1978). https://doi.org/10.1007/BF01109732
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DOI: https://doi.org/10.1007/BF01109732