【摘要】：混合流體力學是一門研究兩種或者多種流體運動規(guī)律和應用的學科.從理論角度,混合流體力學利用質量守恒和動量守恒等規(guī)律,通過精確的數(shù)學模型來描述流體的運動,這個模型就是通常所說的混合流體動力學方程.本文主要研究的混合流體模型包括氣體-液體兩相流模型、流體-質子交互作用模型以及熱力學框架下推導的混合流體模型.主要的結果如下：·研究三維粘性氣體-液體兩相流模型的爆破準則.我們在Dirichlet邊界條件和Navier-slip邊界條件下,證明了粘性氣體兩相流局部強解的速度梯度L1t(Lx∞)范數(shù)在有限時間內的爆破準則.這個結論改進了二維的結果,并且放寬了對粘性系數(shù)的限制條件,即不需要限制粘性系數(shù)入7μ.·研究了流體-質子交互模型在泡沫機制下解的最優(yōu)收斂率問題.得到了當初值在靜態(tài)解附近并且外力項充分小時,整體強解的存在唯一性.在這個基礎上,通過線性化方程的Lp-Lq估計以及精確的能量估計得到了整體強解的最優(yōu)收斂率.·研究了不可壓二維混合流體方程解的整體適定性問題.通過對兩種流體的密度限制為常數(shù)的設定,我們首次得到了簡化模型.首先利用Fridrich方法證明了局部解的存在唯一性.其次,利用經(jīng)典方法得到解的整體適定性.
[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，

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