Global existence of weak solutions for the multicomponent reaction flows

Xi, Xiaoyu; Xie, Binqiang

doi:10.1016/j.jmaa.2016.04.041

Cited by 4 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore we deal with only one equation for the total energy of the whole mixture. To summarize, we consider the following steady version of a model of chemically reacting mixture with n constituents in a bounded smooth domain Ω ⊂ R 3 div ( u) = 0,…”

Section: Formulation Of the Problem Known Resultsmentioning

confidence: 99%

“…Moreover, as we may easily include also a nonzero bulk viscosity with similar form of the viscosity (it is only important that both viscosities are bounded from above and below by C(1 + )), our model differs from the models where the Bresch-Desjardin entropy plays an important role (see Bresch and Desjardins 1 ); such a model was studied for chemically reacting mixtures in the evolutionary case in Mucha et al 2 or Xi and Xie. 3 The pressure consists of two parts: the cold pressure and the molecular pressure; the latter (according to the Dalton law) is the sum of partial pressures p k…”

Section: S(mentioning

confidence: 99%

“…Further results, for more general diffusion matrix, can be found in Zatorska 13 and Zatorska; 14 and in Mucha et al, 15 Mucha et al, 16 and Mucha et al; 2 or in Xi and Xie. 3 In the papers, where also the fluid equations are included, the viscosity is similar to the viscosity studied here. However, here the estimates coming from Bresch-Desjardin entropy play an important role and therefore the precise form of viscosity, which is unfortunately not very relevant from the point of view of physics must be used.…”

Section: S(mentioning

confidence: 99%

See 2 more Smart Citations

Steady solutions to a model of compressible chemically reacting fluid with high density

Axmann

Pokorný

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

We consider a model describing the steady flow of compressible heat-conducting chemically reacting multicomponent mixture. We show the existence of strong solutions under the additional assumption that the mixture is sufficiently dense. We work in the L p -setting combining the methods for the weak solutions with the method of decomposition. The result is a generalization of previous results of the authors, where the case of single-constituted fluid was studied.

show abstract

Section: Formulation Of the Problem Known Resultsmentioning

confidence: 99%

Section: S(mentioning

confidence: 99%

Section: S(mentioning

confidence: 99%

See 1 more Smart Citation

Steady solutions to a model of compressible chemically reacting fluid with high density

Axmann

Pokorný

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Section: Msc Classification: 76n10 35q30mentioning

confidence: 99%

“…This was possible thanks to postulate of the so-called Bresch-Desjardins condition for the viscosity coefficients, which provides an extra estimate of the density gradient and a special form of the pressure. The last restriction was recently removed by Xi and Xie [52].The global well-posedness in the framework of strong solutions for the compressible Navier-Stokes(-Fourier) system under smallness assuptions on the data is already well investigated, see among others [28] in L 2 framework, [48] in L p setting with slip boundary condition or [38,13] for a free boudary problem. However, for the system coupled with reaction-diffusion equations admitting cross-diffusion the issue of global well posedness of initial-boundary value problems has remained open.The purpose of this work is to prove the global in time existence of strong solutions to the system (1.1).…”

mentioning

confidence: 99%

On Strong Dynamics of Compressible Two-Component Mixture Flow

Piasecki

Shibata²,

Zatorska

2019

SIAM J. Math. Anal.

View full text Add to dashboard Cite

We investigate a system describing the flow of a compressible two-component mixture. The system is composed of the compressible Navier-Stokes equations coupled with non-symmetric reactiondiffusion equations describing the evolution of fractional masses. We show the local existence and, under certain smallness assumptions, also the global existence of unique strong solutions in Lp − Lq framework. Our approach is based on so called entropic variables which enable to rewrite the system in a symmetric form. Then, applying Lagrangian coordinates, we show the local existence of solutions applying the Lp-Lq maximal regularity estimate. Next, applying exponential decay estimate we show that the solution exists globally in time provided the initial data is sufficiently close to some constants. The nonlinear estimates impose restrictions 2 < p < ∞, 3 < q < ∞. However, for the purpose of generality we show the linear estimates for wider range of p and q. MSC Classification: 76N10, 35Q30Under the assumption (1.6), global in time strong (unique) solutions around the constant equilibrium for the Cauchy problem was proven by Giovangigli in [19]. He introduced the entropic and normal variables to symmetrize the system (1.1) and applied the Kawashima and Shizuta theory [24,25] for symmetric hyperbolic-parabolic systems of conservation laws. For the local in time existence result to the species mass balances equations in the isobaric, isothermal case we refer to [3], see also [21]. Later on, Jüngel and Stelzer generalized this result and combined it with the entropy dissipation method to prove the global in time existence of weak solutions [23], still in the case of constant pressure and temperature. The detailed description of the method and its applicability for a range of models we refer to [22]. For the qualitative and quantitative analysis of the ternary gaseous system together with numerical simulations we refer to [7]. One should note that constant pressure assumption in (1.5) not only significantly simplifies the cross-diffusion equations but basically decouples the fluid and the reactiondiffusion parts of the system (1.1). Stationary problems for compressible mixtures were considered in [49] under the assumption of Fick law and later in [20,35,36] with cross diffusion, however for different molar masses. Existence of weak solutions for the mixture of non-newtonian fluids has been shown in [8]. Let us also mention results on multi-phase systems [16,26] and incompressible mixtures [27,9,5]. We would also like to mention the theoretical results for the systems describing the compressible reacting electrolytes [11], where the authors prove the existence of global in time weak solutions to the Nernst-Planck-Poisson model originating from the modelling approach developed by Bothe and Dreyer in the previous paper [4]. The classical mixture models in the sense of [19] were studied in the series of papers [50,51,30,31,32], where the global in time existence of weak solutions was proved without any simplification of (1.7). This was...

show abstract

Consequence analysis of derivative accidents due to reaction runaway

Liu

Jiang

et al. 2018

Journal of Loss Prevention in the Process Industries

View full text Add to dashboard Cite

Global existence of weak solutions for the multicomponent reaction flows

Cited by 4 publications

References 16 publications

Steady solutions to a model of compressible chemically reacting fluid with high density

Steady solutions to a model of compressible chemically reacting fluid with high density

On Strong Dynamics of Compressible Two-Component Mixture Flow

Consequence analysis of derivative accidents due to reaction runaway

Contact Info

Product

Resources

About