论文标题
从扩散缩放中的多物种玻尔兹曼方程中给给跨跨扩散系统的严格推导
Rigorous derivation of the Fick cross-diffusion system from the multi-species Boltzmann equation in the diffusive scaling
论文作者
论文摘要
我们以Sobolev空间严格的方式呈现了来自多物种玻尔兹曼的流体混合物的给质合交叉扩散系统的产生。为此，我们正式表明，在扩散缩放的情况下，动力学系统的流体动力学极限是补充闭合关系的给给给给宽度的模型，我们给出了从玻璃体碰撞算子的宏观扩散系数的明确配方。然后，我们在构造的给给系统的Sobolev空间中提供了一种扰动的Cauchy理论，事实证明这是扩张的抛物线方程。我们最终证明了系统在Boltzmann方程中的稳定性，从而确保了两个模型之间的严格推导。
We present the arising of the Fick cross-diffusion system of equations for fluid mixtures from the multi-species Boltzmann in a rigorous manner in Sobolev spaces. To this end, we formally show that, in a diffusive scaling, the hydrodynamical limit of the kinetic system is the Fick model supplemented with a closure relation and we give explicit formulae for the macroscopic diffusion coefficients from the Boltzmann collision operator. Then, we provide a perturbative Cauchy theory in Sobolev spaces for the constructed Fick system, which turns out to be a dilated parabolic equation. We finally prove the stability of the system in the Boltzmann equation, ensuring a rigorous derivation between the two models.
