Title: Non-isentropic cavity flow for the multi-d compressible Euler system Show Chinese title

Title: 非等熵腔流对于多维可压缩欧拉系统

Abstract: We rigorously construct non-isentropic and self-similar multi-d Euler flows in which a central cavity (vacuum region) collapses. While isentropic flows of this type have been analyzed earlier by Hunter \cite{hun_60} and others, the non-isentropic setting introduces additional complications, in particular with respect to the behavior along the fluid-vacuum interface. The flows we construct satisfy the physical boundary conditions: the interface is a material surface along which the pressure vanishes, and it propagates with a non-vanishing and finite acceleration until collapse. We introduce a number of algebraic conditions on the parameters in the problem (spatial dimension, adiabatic index, similarity parameters). With these conditions satisfied, a simple argument based on trapping regions for the associated similarity ODEs yields the existence of non-isentropic cavity flows. We finally verify that the conditions are all met for several physically relevant cases in both two and three dimensions. Show Chinese abstract

Abstract: 我们严格构造了非等熵和自相似的多维欧拉流，其中心腔（真空区域）发生坍缩。 虽然此类等熵流之前已由Hunter\cite{hun_60}和其他人分析过，但非等熵情形引入了额外的复杂性，特别是关于流体-真空界面的行为。 我们构造的流体满足物理边界条件：界面是一个物质表面，压力在此处消失，并以非零且有限的加速度传播直到坍缩。 我们对问题中的参数（空间维度、绝热指数、相似性参数）引入了一些代数条件。 在满足这些条件的情况下，基于相关相似性常微分方程的 trapping 区域的简单论证可以得出非等熵腔流的存在性。 最后，我们验证了在二维和三维的几种物理上相关的案例中，所有条件都得到了满足。