论文标题
与Maxwell-Stefan扩散的理想气体混合物的通用解决方案理论
A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion
论文作者
论文摘要
在Giovangigli在多组分流数学上的开创性工作之后，进行了几次尝试为PDE引入全局弱解决方案，以描述流体混合物的动力学。尽管由于Chen和Jüngel（等温病例）或Marion和Temam的结果，恒定密度的不可压缩病的启发得很好，但对于较弱的气体混合溶液理论及其相应的混合抛物线抛物性 - 应贝 - 透明透碳类型的弱解决方案理论仍然存在一些开放性问题。例如，Mucha，Pokorny和Zatorska表明了通过Bresch-Desjardins技术和防止真空的压力正规化稳定双曲线成分的可能性。 Dreyer，Druet，Gajewski和Guhlke的结果避免了Machina的稳定，但是数学假设是，Onsager矩阵对某些子空间的引线均匀地呈稀释极限，以稀释的极限，对无限的扩散速度与Maxwell-Stefan for giffusion diffusifus Fluxs不兼容。在本文中，我们证明了具有自然扩散的等温和理想压缩混合物的全球弱解。主要的新工具是在低压下对二进制麦克斯韦 - 斯特凡扩散性施加的渐近条件，这可以补偿稀有溶液在稀有方案中的极端行为。
After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for the PDEs describing the dynamics of fluid mixtures. While the incompressible case with constant density was enlighted well enough due to results by Chen and Jüngel (isothermal case), or Marion and Temam, some open questions remain for the weak solution theory of gas mixtures with their corresponding equations of mixed parabolic-hyperbolic type. For instance, Mucha, Pokorny and Zatorska showed the possibility to stabilise the hyperbolic component by means of the Bresch-Desjardins technique and a regularisation of pressure preventing vacuum. The result by Dreyer, Druet, Gajewski and Guhlke avoids ex machina stabilisations, but the mathematical assumption that the Onsager matrix is uniformly positive on certain subspaces leads, in the dilute limit, to infinite diffusion velocities which are not compatible with the Maxwell-Stefan form of diffusion fluxes. In this paper, we prove the existence of global weak solutions for isothermal and ideal compressible mixtures with natural diffusion. The main new tool is an asymptotic condition imposed at low pressure on the binary Maxwell-Stefan diffusivities, which compensates possibly extreme behaviour of weak solutions in the rarefied regime.
