Mathematical Sciences: Mathematical Problems in CompressibleFluid Flow

根据这项提议，主要研究者将继续 他对不连续解的分析和数值研究 的数学模型的粘性，可压缩流在两个和 三维空间 特别是，他将调查 方程组边值问题的适定性 非线性双曲方程的模型，他 将设计改进的数值方案， 解决方案中存在的不连续性。 数学家和流体力学家经常研究一个- 复杂流动现象的三维模型，以获得 对两个和三个空间中的真实的流行为的洞察 尺寸. 在本补助金中，主要研究人员将 扩展了他的一些结果的一维模型的 气体动力学方程更现实的模型在更高的 尺寸. 不止一维的问题是困难的， 所以研究人员会使用一个综合分析- 研究不连续解的数值方法，称为 “震惊”。

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".