A multifluid model with chemically reacting components – construction of weak solutions. (English) Zbl 07916209
Summary: We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of irreversible chemical reactions and assume a nonlinear relation between the pressure and the particular densities. These assumptions cause the additional difficulties in the mathematical analysis, due to the possible presence of vacuum.
It is shown that there exists a global weak solution, satisfying the \(L^\infty\) bounds for all the components. We obtain strong compactness of the sequence of densities in \(L^p\) spaces, under the assumption that all components are strictly positive. The applied method captures the properties of models of high generality, which admit an arbitrary number of components. Furthermore, the framework that we develop can handle models that contain both diffusing and non-diffusing elements.
It is shown that there exists a global weak solution, satisfying the \(L^\infty\) bounds for all the components. We obtain strong compactness of the sequence of densities in \(L^p\) spaces, under the assumption that all components are strictly positive. The applied method captures the properties of models of high generality, which admit an arbitrary number of components. Furthermore, the framework that we develop can handle models that contain both diffusing and non-diffusing elements.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76V05 | Reaction effects in flows |
| 35D30 | Weak solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
Keywords:
compressible Stokes system; multi-component flow; weak solutions; irreversible chemical reactionReferences:
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