论文标题
流体混合物的不可压缩极限
Incompressible limit for a fluid mixture
论文作者
论文摘要
在本文中，我们讨论了等温理想情况下多组分流体的不可压缩极限。研究了状态方程中的直接限制和重新定量PDE中的低声音限制。使用相对能量不等式，我们在不可压缩模型具有足够光滑的溶液的条件下获得了密度和速度场的收敛结果，至少在很短的时间内授予。此外，与单组分流相比，在多组分情况下需要均匀的估计和压力的收敛，因为不可压缩的速度场并非无差异。我们表明，迁移率张量的某些星座允许控制熵变量的梯度并产生L1压力的收敛性。
In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.
