Two-velocity hydrodynamics in fluid mechanics: Part I Well posedness for zero Mach number systems
Two-velocity hydrodynamics in fluid mechanics: Part I Well posedness for zero Mach number systems
复制标题
DOI：
10.1016/j.matpur.2015.05.003
复制
发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
D. Bresch;V. Giovangigli;E. Zatorska
中科院分区：
文献类型：
--
作者：
D. Bresch;V. Giovangigli;E. Zatorska
本文证明了流体力学中具有周期边界条件的零马赫数方程组弱解的整体存在性。放松[6]中引入的粘度和电导率之间的某种代数约束，对[23]中提出的一个公开问题给出了更完整的答案。我们引入了一个新的数学熵，它清楚地表明存在的双速流体动力学与固定的混合比。作为我们结果的应用，我们首先讨论了一个气体混合模型，将[10]的结果推广到整体弱解框架。其次，介绍了C.D. Levermore，W. Sun和K. Trivisa [20]的结果，并讨论了密度相关的导热系数对弱解存在性问题的贡献。
In this paper we prove global in time existence of weak solutions to zero Mach number systems arising in fluid mechanics with periodic boundary conditions. Relaxing a certain algebraic constraint between the viscosity and the conductivity introduced in [6] gives a more complete answer to an open question formulated in [23]. We introduce a new mathematical entropy which clearly shows existence of two-velocity hydrodynamics with a fixed mixture ratio. As an application of our result we first discuss a model of gaseous mixture extending the results of [10] to the global weak solutions framework. Second, we present the ghost effect system studied by C.D. Levermore, W. Sun and K. Trivisa [20] and discuss a contribution of the density-dependent heat-conductivity coefficient to the issue of existence of weak solutions.