Analysis of an Incompressible Navier–Stokes–Maxwell–Stefan System

Chen, Xiuqing; Jüngel, Ansgar

doi:10.1007/s00220-015-2472-z

Cited by 48 publications

(96 citation statements)

References 18 publications

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“…It was also proven, independently in [10] and [25], that the incompressible Navier-Stokes-Stefan-Maxwell system possesses a global-in-time weak solution with arbitrary data . The approach employed by Chen and Jüngel in [10] relies on a certain symmetrization of the species subsystem with one of equations eliminated, see also [22]. They have noticed that such reformulation allows to deduce parabolicity in terms of the socalled entropic variables.…”

Section: Discussion Of the Known Resultsmentioning

confidence: 93%

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On the isothermal compressible multi-component mixture flow: The local existence and maximalLp−Lqregularity of solutions

2019

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We consider the initial-boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier-Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in [35], we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal L p − L q regularity of solutions.

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Section: Discussion Of the Known Resultsmentioning

confidence: 93%

“…Using expressions for the diffusion forces (10) and the properties of this matrix one can rewrite (7) into the following form…”

Section: Diffusion Fluxesmentioning

confidence: 99%

On the isothermal compressible multi-component mixture flow: The local existence and maximalLp−Lqregularity of solutions

2019

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“…[13]), the mathematical and numerical analysis started more recently [1,16]. The global existence of weak solutions under natural conditions was proved in [6,21] for neutral mixtures. In case of ion transport, the electric charges and the self-consistent electric potential need to be taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…This means that the mixture cannot leave the container Ω and an electric field is applied at the contacts Γ N . The initial conditions are given by (6) ρ i (·, 0) = ρ 0 i in Ω, i = 1, . .…”

Section: Introductionmentioning

confidence: 99%

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Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems

Jüngel

Leingang

2019

Adv Comput Math

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A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the diffusive dynamics of an isothermal ionized fluid mixture with vanishing barycentric velocity. The equations are studied in a bounded domain, and different molar masses are allowed. The Galerkin scheme preserves the total mass, the nonnegativity of the particle densities, their boundedness, and satisfies the second law of thermodynamics in the sense that the discrete entropy production is nonnegative. The existence of solutions to the Galerkin scheme and the convergence of a subsequence to a solution to the continuous system is proved. Compared to previous works, the novelty consists in the treatment of the drift terms involving the electric field. Numerical experiments show the sensitive dependence of the particle densities and the equilibration rate on the molar masses.

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