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Journal of Mathematical Sciences

, Volume 198, Issue 6, pp 761–827 | Cite as

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

  • V. A. Solonnikov
Article

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.

Keywords

Linear Problem Orthogonality Condition Free Boundary Problem Homogeneous Problem Steklov Inst 
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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical Institute RASSt. PetersburgRussia

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