带Korteweg项的流体方程的解的研究
发布时间：2019-07-05 18:18
【摘要】：本文主要内容分为两部分,第一部分考虑具阻尼的Euler-Korteweg方程的解的渐近行为,得到当时间充分大时,方程的解收敛到非线性扩散波,并得到相应的收敛率;进而证明当Korteweg系数收敛于零时,具阻尼Euler-Korteweg方程收敛于具阻尼的Euler方程.第二部分主要证明在一维空间中带Korteweg项的两相流模型的弱解的整体存在性.第一部分在证明过程中,通过具阻尼的Euler-Korteweg方程及Darcy定律的性质得到校正函数的表达式,从而将具阻尼的Euler-Korteweg方程化简为一个新的方程,再通过构造非线性扩散方程的自相似解,得到非线性扩散方程的解的耗散估计,进而将研究Euler-Korteweg方程收敛到非线性扩散波的收敛估计转化为研究新的方程收敛到零的衰减估计.第二部分证明主要采用了能量估计的方法证明了带Korteweg项的两相流模型的弱解的整体存在性.
[Abstract]:The main content of this paper is divided into two parts. In the first part, the asymptotic behavior of the solution of the damped Euler-Korteweg equation is considered, and the solution of the equation converges to the nonlinear diffusion wave when the time is large enough, and the corresponding convergence rate is obtained, and then it is proved that when the Korteweg coefficient converges to 00:00, the damped Euler-Korteweg equation converges to the damped Euler equation. In the second part, we mainly prove the global existence of weak solutions of two-phase flow model with Korteweg term in one-dimensional space. In the first part, through the properties of damped Euler-Korteweg equation and Darcy law, the expression of correction function is obtained, and the damped Euler-Korteweg equation is reduced to a new equation, and then the dissipative estimation of the solution of nonlinear diffusion equation is obtained by constructing the self-similar solution of nonlinear diffusion equation. Furthermore, the convergence estimation of the Euler-Korteweg equation to the nonlinear diffusion wave is transformed into the attenuation estimation of the new equation converging to zero. In the second part, we prove the global existence of the weak solution of the two-phase flow model with Korteweg term by using the energy estimation method.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2510722
[Abstract]:The main content of this paper is divided into two parts. In the first part, the asymptotic behavior of the solution of the damped Euler-Korteweg equation is considered, and the solution of the equation converges to the nonlinear diffusion wave when the time is large enough, and the corresponding convergence rate is obtained, and then it is proved that when the Korteweg coefficient converges to 00:00, the damped Euler-Korteweg equation converges to the damped Euler equation. In the second part, we mainly prove the global existence of weak solutions of two-phase flow model with Korteweg term in one-dimensional space. In the first part, through the properties of damped Euler-Korteweg equation and Darcy law, the expression of correction function is obtained, and the damped Euler-Korteweg equation is reduced to a new equation, and then the dissipative estimation of the solution of nonlinear diffusion equation is obtained by constructing the self-similar solution of nonlinear diffusion equation. Furthermore, the convergence estimation of the Euler-Korteweg equation to the nonlinear diffusion wave is transformed into the attenuation estimation of the new equation converging to zero. In the second part, we prove the global existence of the weak solution of the two-phase flow model with Korteweg term by using the energy estimation method.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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