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L p -Theory of the Problem of Motion of Two Incompressible Capillary Fluids in a Container

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We prove the L p -estimates for the solution of the problem of motion of two immiscible viscous incompressible capillary fluids in a container. The fluids are subject to the mass forces exponentially decaying as t → ∞. Recently, this problem (with vanishing external forces) was studied in the Hölder spaces of functions. We prove the solvability of the problem with the initial data close to the equilibrium state and analyze the behavior of the solution as t → ∞. We also discuss the case of absence of the surface tension. Bibliography: 42 titles.

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  1. St. Petersburg Department of the Steklov Mathematical Institute RAS, 27, Fontanka Str., St. Petersburg, 191023, Russia

    V. A. Solonnikov

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Translated from Problemy Matematicheskogo Analiza 75, April 2014, pp. 93–152.

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Solonnikov, V.A. L p -Theory of the Problem of Motion of Two Incompressible Capillary Fluids in a Container. J Math Sci 198, 761–827 (2014). https://doi.org/10.1007/s10958-014-1824-0

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