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- W4286585352 abstract "This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain $Omegasubset mathbb{R}^d$, $d=2,3$. We focus on dissipative mixing effects originating from the mass-conserving Allen-Cahn dynamics with the physically relevant Flory-Huggins potential. More precisely, we study the mass-conserving Navier-Stokes-Allen-Cahn system for nonhomogeneous fluids and the mass-conserving Euler-Allen-Cahn system for homogeneous fluids. We prove existence and uniqueness of global weak and strong solutions as well as their property of separation from the pure states. In our analysis, we combine the energy and entropy estimates, a novel end-point estimate of the product of two functions, a new estimate for the Stokes problem with non-constant viscosity, and logarithmic type Gronwall arguments." @default.
- W4286585352 created "2022-07-22" @default.
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- W4286585352 date "2020-05-14" @default.
- W4286585352 modified "2023-09-25" @default.
- W4286585352 title "On the Mass-Conserving Allen-Cahn Approximation for Incompressible Binary Fluids" @default.
- W4286585352 doi "https://doi.org/10.48550/arxiv.2005.07236" @default.
- W4286585352 hasPublicationYear "2020" @default.
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