关于混合流体力学中一些问题的研究
发布时间：2018-08-03 19:02
【摘要】：混合流体力学是一门研究两种或者多种流体运动规律和应用的学科.从理论角度,混合流体力学利用质量守恒和动量守恒等规律,通过精确的数学模型来描述流体的运动,这个模型就是通常所说的混合流体动力学方程.本文主要研究的混合流体模型包括气体-液体两相流模型、流体-质子交互作用模型以及热力学框架下推导的混合流体模型.主要的结果如下：·研究三维粘性气体-液体两相流模型的爆破准则.我们在Dirichlet边界条件和Navier-slip边界条件下,证明了粘性气体两相流局部强解的速度梯度L1t(Lx∞)范数在有限时间内的爆破准则.这个结论改进了二维的结果,并且放宽了对粘性系数的限制条件,即不需要限制粘性系数入7μ.·研究了流体-质子交互模型在泡沫机制下解的最优收敛率问题.得到了当初值在静态解附近并且外力项充分小时,整体强解的存在唯一性.在这个基础上,通过线性化方程的Lp-Lq估计以及精确的能量估计得到了整体强解的最优收敛率.·研究了不可压二维混合流体方程解的整体适定性问题.通过对两种流体的密度限制为常数的设定,我们首次得到了简化模型.首先利用Fridrich方法证明了局部解的存在唯一性.其次,利用经典方法得到解的整体适定性.
[Abstract]:Hybrid fluid dynamics is a subject that studies the motion laws and applications of two or more kinds of fluids. From a theoretical point of view, hybrid fluid dynamics uses the laws of mass conservation and momentum conservation to describe the motion of the fluid through an accurate mathematical model, which is commonly referred to as the mixed fluid dynamic equation. In this paper, the mixed fluid model is mainly studied, including the gas-liquid two-phase flow model, the fluid-proton interaction model and the hybrid fluid model derived under the thermodynamic framework. The main results are as follows: the blasting criterion of three-dimensional viscous gas-liquid two-phase flow model is studied. Under Dirichlet boundary condition and Navier-slip boundary condition, we prove the blow-up criterion of velocity gradient L 1t (LX 鈭，
本文编号：2162707
[Abstract]:Hybrid fluid dynamics is a subject that studies the motion laws and applications of two or more kinds of fluids. From a theoretical point of view, hybrid fluid dynamics uses the laws of mass conservation and momentum conservation to describe the motion of the fluid through an accurate mathematical model, which is commonly referred to as the mixed fluid dynamic equation. In this paper, the mixed fluid model is mainly studied, including the gas-liquid two-phase flow model, the fluid-proton interaction model and the hybrid fluid model derived under the thermodynamic framework. The main results are as follows: the blasting criterion of three-dimensional viscous gas-liquid two-phase flow model is studied. Under Dirichlet boundary condition and Navier-slip boundary condition, we prove the blow-up criterion of velocity gradient L 1t (LX 鈭，
本文编号：2162707
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