Multicomponent reactive flows: Global-in-time existence for large data

Feireisl, Eduard; Petzeltová, Hana; Trivisa, Konstantina

doi:10.3934/cpaa.2008.7.1017

Cited by 55 publications

(68 citation statements)

References 18 publications

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“…Concerning analogous results for the compressible Navier-Stokes-Stefan-Maxwell system, the existence of weak solutions is so far known either for stationary flow of species with the same molar masses [43,19,32,33], or for exemplary diffusion matrix C and stress tensor S with density-dependent viscosity coefficient [44,45,28,29]. There are also relevant results for multi-component systems with diffusion fluxes in the form of the Fick law [14].…”

Section: Discussion Of the Known Resultsmentioning

confidence: 98%

“…In both of these papers the isobaric isothermal systems are considered with the barycentric velocity being equal to 0. This means that, in comparison with the system of last n equations from (1), the convective term div(̺ k u) is absent and the variation of total pressure in the diffusion fluxes (14) is neglected. Essential difference between these systems is that in the present case the diffusion fluxes are explicit combination of diffusion deriving forces, while for the Stefan-Maxwell system the flux-forces relations need to be first inverted.…”

Section: Discussion Of the Known Resultsmentioning

confidence: 99%

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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: 98%

Section: Discussion Of the Known Resultsmentioning

confidence: 99%

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

2019

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“…Substituting in (14) p k = e r k,N and = N we deduce that the last term on the right hand side of (29) is bounded…”

Section: A Galerkin Approximationmentioning

confidence: 96%

Chemically reacting mixtures in terms of degenerated parabolic setting

Mucha

Pokorný

Zatorska

2013

Journal of Mathematical Physics

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Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic modelThe paper analyzes basic mathematical questions for a model of chemically reacting mixtures. We derive a model of several (finite) component compressible gas taking rigorously into account the thermodynamical regime. Mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation. The thermodynamics implies that the diffusion terms are non-symmetric, not positively defined, and cross-diffusion effects must be strongly marked. The mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species. A key point is an entropy-like estimate showing possible renormalization of the system. C 2013 AIP Publishing LLC.

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“…A more general pressure form can be assumed, as in the case of the steady compressible Navier-Stokes-Fourier system, see e.g. [11] or [2] in the context of the chemically reacting flows. We, however, prefer to keep its form as simple as possible.…”

Section: Introductionmentioning

confidence: 99%

On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions

Piasecki¹,

Pokorný²

2018

Mathematical Analysis in Fluid Mechanics

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We consider a model of chemically reacting heat conducting compressible mixture. We investigate the corresponding system of partial differential equations in the steady regime with slip boundary conditions for the velocity and, in dependence on the model parameters, we establish existence of either weak or variational entropy solutions. The results extend the range of parameters for which the existence of weak solutions is known in the case of homogeneous Dirichlet boundary conditions for the velocity.1991 Mathematics Subject Classification. Primary 76N10 Secondary 35Q30 .

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Multicomponent reactive flows: Global-in-time existence for large data

Cited by 55 publications

References 18 publications

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

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

Chemically reacting mixtures in terms of degenerated parabolic setting

On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions

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