本项目研究可压流体的熵逼近和带有边界小粘性流体的边界层问题,这是流体力学专家研究与探索的热点和难点问题之一.本项目的研究内容如下:1.拟通过时间衰减估计的方法来研究非等熵可压缩Navier-Stokes(NS)方程组的熵逼近;2.拟通过稳定性估计方法来研究小粘性NS方程的边界层展开理论,重点探索密度变化、区域边界弯曲效应和磁场对其产生的影响;3.拟通过能量模方法在索伯列夫空间中研究非定常小粘性流体的边界层方程的适定性问题,探索密度变化、维数增加和穿透磁场所产生的影响.本项目的目标是从数学角度合理解释非等熵可压缩NS方程的熵逼近问题,构建小粘性流体的边界层数学理论.本项目拟解决的关键科学问题是:1.选择合适的方式建立等熵可压缩NS方程组和非等熵可压缩NS方程组两者之间的联系,从而证明熵逼近的合理性;2.处理好退化抛物方组以及双曲退化抛物的切向导数丢失问题.

Entropy approximation of compressible fluids and boundary layer problem of small viscous fluids with boundary are two hot and difficult problems in fluid mechanics research and exploration. The research contents of this project are as follows: 1. Entropy approximation of Nonisentropic compressible Navier-Stokes (NS) equations is to be studied by time decay estimation method; 2. Stability estimation method is to be used to study small viscous NS equations. The boundary layer expansion theory of NS equation focuses on the density change, the bending effect of the regional boundary and the influence of the magnetic field on it;3. The appropriateness of the boundary layer equation for unsteady small viscous fluids is studied in Sobolev space by means of the energy model method, and the effects of density change, dimension increase and penetrating magnetic field are explored. The objective of this project is to explain reasonably the entropy approximation problem of Non-isentropic compressible NS equation from a mathematical point of view, and constructe the boundary layer mathematical theory for the small viscous fluids. The key scientific problems to be solved in this project are as follows: 1. Choosing appropriate ways to establish the relationship between isentropic compressible NS equation and Non-isentropic compressible NS equation, so as to prove the rationality of entropy approximation; 2. Dealing with the estimate of loss horizontal derivatives for the degenerate parabolic systems and hyperbolic degenerate parabolic coupling systems.