电磁流体力学方程组的适定性和渐近机制研究

项目名称： 电磁流体力学方程组的适定性和渐近机制研究

项目编号： No.U1204103

项目类型： 联合基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 杨建伟

作者单位： 华北水利水电大学

项目金额： 30万元

中文摘要： 本项目主要研究电磁流体力学中非线性偏微分方程组及其相关流体动力学模型的适定性和渐近极限问题，将运用调整能量方法、多尺度渐近分析、奇异摄动分析和相对熵等方法重点研究这些模型的渐近机制（如大时间行为、扩散松弛极限、非相对论极限、零电子质量极限、拟中性极限以及解的多尺度结构稳定性等）。期望通过组建一系列行之有效的一致先验估计，从数学层面上解释电磁流体力学方程组与各种相关的流体动力学模型之间的本质联系，并对理论结果进行数值模拟和分析。本课题将推动Euler方程和Navier-Stokes方程等模型正则性的进展。 本项目是国际非线性发展方程组研究领域的前沿课题，有重要的理论意义和较强的应用背景。

中文关键词： 电磁流体力学方程组；渐近极限；适定性；收敛估计；

英文摘要： This project is devoted to the study on well-posedness and asymptotic limits of the nonlinear partial differential equations and related hydrodynamics models in the electromagnetic hydrodynamics. Our research focus on the asymptotic regimes (such as large time behavior, diffusion relaxation limit, non-relativistic limit, zero electron mass limit, quasi-neutral limit and multi-scale structure stability of the solutions) by using a weighted energy method, multi-scale asymptotic analysis, singular perturbation analysis and relative entropy theory. We expect to obtain the mathematical explanations of the essential relations between the electromagnetic hydrodynamics equations and the other related hydrodynamics models by establishing a series of effective uniform priori estimates. And a numerical simulation and analysis will be carried on the theoretical results. The task will promote the advance of the regularity of Euler equations, Navier-Stokes equations, and so on. This project belongs to the frontier subject of the study on nonlinear evolution equations in the world. It is of important theoretical significance and better application background.

英文关键词： EMHD Equations；Asymptotic Limit；Well-posedness；Convergence Estimate；