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On Varifold Solutions of Two-Phase Incompressible Viscous Flow with Surface Tension

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Abstract

In this paper using diffuse approximations the existence of a varifold solution to the two-phase Newtonian incompressible viscous flow problem is derived. On the free surface between the two phases we consider surface tension force. Also we prove that for axisymmetric, possibly with swirl, initial velocities and cylindrically symmetric initial volumes occupied by each fluid there exists a global in time axisymmetric, with swirl, solution.

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  1. Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Karen Yeressian

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  1. Karen Yeressian
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Correspondence to Karen Yeressian.

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Communicated by K. Pileckas

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Yeressian, K. On Varifold Solutions of Two-Phase Incompressible Viscous Flow with Surface Tension. J. Math. Fluid Mech. 17, 463–494 (2015). https://doi.org/10.1007/s00021-015-0217-6

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  • DOI: https://doi.org/10.1007/s00021-015-0217-6

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