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Two phase flows of compressible viscous fluids

  • * Corresponding author: Eduard Feireisl

    * Corresponding author: Eduard Feireisl 

The work of E.F. was supported by the Czech Sciences Foundation (GAČR), Grant Agreement 21–02411S.

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  • We introduce a new concept of dissipative varifold solution to models of two phase compressible viscous fluids. In contrast with the existing approach based on the Young measure description, the new formulation is variational combining the energy and momentum balance in a single inequality. We show the existence of dissipative varifold solutions for a large class of general viscous fluids with non–linear dependence of the viscous stress on the symmetric velocity gradient.

    Mathematics Subject Classification: Primary: 35Q35, 35A30; Secondary: 35D30.

    Citation:

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  • [1] A. AbbatielloE. Feireisl and A. Novotný, Generalized solutions to models of compressible viscous fluids, Discrete Contin. Dyn. Syst., 41 (2021), 1-28.  doi: 10.3934/dcds.2020345.
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    [4] D. M. AmbroseM. C. Lopes FilhoH. J. Nussenzveig Lopes and W. A. Strauss, Transport of interfaces with surface tension by 2D viscous flows, Interfaces Free Bound., 12 (2010), 23-44.  doi: 10.4171/IFB/225.
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    [10] J. Fischer and S. Hensel, Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension, Arch. Rational Mech. Anal., 236 (2020), 967-1087.  doi: 10.1007/s00205-019-01486-2.
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