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arXiv · 1509.05663

Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities

Helmut Abels·Dominic Breit
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Abstract

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the $L^\infty$-truncation method we prove existence of weak solutions for a power-law exponent $p>\frac{2d+2}{d+2}$, $d=2,3$.

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Helmut Abels, Dominic Breit. 2016-06-26. Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities. https://doi.org/10.1088/0951-7715%2F29%2F11%2F3426

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