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Certain nonlocal problems for two-dimensional equations of motion of Oldroyd fluids

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Abstract

The solvability of a boundary-value problem on the semi-axis t≥0 is studied for two-dimensional equations of motion of Oldroyd fluids (1), and with “trivial problem data” a proof is given of the existence of a solution which is periodic with respect to t and has the period ω. This solution has an absolute term which is also periodic with respect to t and has the period ω. Substantiation is given for the principle of linearization (first Liapunov method) in the theory of the exponential stability of solutions at t→∞.

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Authors
  1. A. P. Oskolkov
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  2. D. V. Emel'yanova
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 101–121, 1991.

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Oskolkov, A.P., Emel'yanova, D.V. Certain nonlocal problems for two-dimensional equations of motion of Oldroyd fluids. J Math Sci 62, 3004–3016 (1992). https://doi.org/10.1007/BF01097499

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  • DOI: https://doi.org/10.1007/BF01097499

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