论文标题
多组分不可压缩流模型的适应性分析
Well-posedness analysis of multicomponent incompressible flow models
论文作者
论文摘要
在本文中，我们将对多组分等热流体中的质量传输的研究扩展到不可压缩的情况。对于混合物，不可压缩性定义为压力平均体积的独立性，而部分质量密度的加权总和保持恒定。在这种类型的模型中，Navier-Stokes方程中的速度场不是电磁阀，并且由于物种的不同特异性体积，压力仍然通过代数公式连接到密度。通过转运问题中的变量的改变，我们等效地重新重新重新制定了PDE系统，以消除影响密度的阳性和不可压缩性约束，并证明了两种结果的结果：强大解决方案类别中的局部及时及时性，以及全球 - 全球时间存在的解决方案的存在，以实现足够接近平稳的平衡解决方案。
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier-Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.
