Mathematical Sciences: Mathematical Problems in CompressibleFluid Flow

有了这个建议，首席研究员将继续他在二维和三维空间中粘性可压缩流动数学模型的不连续解的分析和数值研究。特别是，他将研究由模型产生的非线性双曲方程系统的边值问题的适定性，他将设计改进的数值格式来解决解中存在的不连续性。数学家和流体动力学家经常研究复杂流动现象的一维模型，以便深入了解二维和三维空间中真实流动的行为。在目前的资助中，首席研究员将把他对一维气体动力学方程模型的一些结果扩展到更现实的高维模型中。超过一个维度的问题是困难的，因此研究者将采用分析-数值相结合的方法来研究称为“冲击”的不连续解。

With this proposal the principal investigator will continue his analytical and numerical studies of discontinuous solutions of mathematical models of viscous, compressible flows in two and three space dimensions. In particular, he will investigate the well-posedness of the boundary value problems for the systems of nonlinear hyperbolic equations resulting from the models, and he will design improved numerical schemes for resolving the discontinuities present in the solutions. Very often mathematicians and fluid dynamicists study one- dimensional models of complicated flow phenomena in order to gain insights into the behavior of real flows in two and three space dimensions. In the present grant the principal investigator will extend some of his results for one-dimensional models of the gasdynamic equations to more realistic models in higher dimensions. Problems in more than one dimension are difficult, and so the investigator will employ a combined analytical- numerical approach to study discontinuous solutions called "shocks".