Two phase flows of compressible viscous fluids

Eduard Feireisl; Antonín Novotný

doi:10.3934/dcdss.2022091

Article Contents

2022, Volume 15, Issue 8: 2215-2232. Doi: 10.3934/dcdss.2022091

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Two phase flows of compressible viscous fluids

Eduard Feireisl^1, , and
Antonín Novotný^2,

1.
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic
2.
IMATH, EA 2134, Université de Toulon, BP 20132, 83957 La Garde, France

^* Corresponding author: Eduard Feireisl
^* Corresponding author: Eduard Feireisl

Received: July 2021

Revised: March 2022

Published: August 2022

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

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Abstract

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.

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

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References

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