高维可压缩非等熵流体力学方程相关问题研究

项目名称： 高维可压缩非等熵流体力学方程相关问题研究

项目编号： No.11471028

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 黎勇

作者单位： 北京工业大学

项目金额： 60万元

中文摘要： 本项目主要研究含热传导效应的高维可压缩非等熵Navier-Stokes方程组及其耦合方程组大初值问题弱解的整体适定性和小参数奇异渐近极限等问题，包括高维可压缩非等熵Navier-Stokes方程组大初值弱解的整体存在性、唯一性、解的大时间渐近行为以及奇异渐近极限，高维可压缩非等熵磁流体力学方程组大初值问题弱解的整体适定性，同时我们还将开展高维可压缩非等熵MHD方程组和Navier-Stokes-Poisson方程组奇异渐近极限问题的研究。高维可压缩非等熵Navier-Stokes方程组及其耦合组具有双曲-抛物耦合、退化性、强非线性以及强耦合的特点，使得其数学理论研究有很大的难度，极具挑战性。本项目的研究内容具有坚实的应用背景和重要的理论意义。

中文关键词： 非等熵纳维-斯托克斯方程组；非等熵磁流体力学方程组；可压缩流体；适定性；奇异极限

英文摘要： The global wellposedness of weak solutions to the multidimensional compressible nonisentropic Navier-Stokes equations and its coupling systems with heat conduction and large initial data will be studied in this project, as well as the singular limits of solutios will be investigated. Precisely, we shall consider the global existence, uniqueness and large time behavior of weak solutions to the multi-dimensional compressible nonisentropic Navier-Stokes equations with large initial data, the singular limits of solutions to the system, and the global wellposedness of weak solutions to the nonisentropic compressible MHD equations with large initial data. At the same time, the singular asymptotic limits of the multidimensional compressible nonisentropic MHD equations and Navier-Stokes-Poisson equations will also be carried out.Due to their degeneration, strong nonlinear and hyperbolic-parabolic coupling, the mathematical analysis of the multidimensional compressible nonisentropic Navier -Stokes equations and its coupling systems are very hard and challenging. This project has strong practical background and theoretical significance.

英文关键词： nonisentropic Navier-Stokes equations;nonisentropic MHD equations;compressible fluid;wellposdness;singular limits