论文标题
在雷利 - 泰勒次树立的最小动作原理中出现的否定性椭圆问题上
On a degenerate elliptic problem arising in the least action principle for Rayleigh-Taylor subsolutions
论文作者
论文摘要
我们解决了一个退化的椭圆形变异问题，该问题在将最小动作原理应用于Boussinesq近似中的不均匀Euler方程的平均溶液中，从水平平坦的雷利 - 泰勒构型产生。我们从与Euler方程相关的差分包含开始，即平均解决方案的概念是在凸集成的背景下的订阅之一，并说明如何将其与Brenier在\ cite frenier引入\ cite {Brenier89，brenier18}。关于对功能本身的调查，我们使用规则近似值来表明具有部分规律性的迷你仪以及对最小化器引起的实际Euler溶液构建重要的其他特性。此外，我们讨论了将最小动作原则在次要的情况下的应用在多大程度上可以用作选择标准。
We address a degenerate elliptic variational problem arising in the application of the least action principle to averaged solutions of the inhomogeneous Euler equations in Boussinesq approximation emanating from the horizontally flat Rayleigh-Taylor configuration. We give a detailed derivation of the functional starting from the differential inclusion associated with the Euler equations, i.e. the notion of an averaged solution is the one of a subsolution in the context of convex integration, and illustrate how it is linked to the generalized least action principle introduced by Brenier in \cite{Brenier89,Brenier18}. Concerning the investigation of the functional itself, we use a regular approximation in order to show the existence of a minimzer enjoying partial regularity, as well as other properties important for the construction of actual Euler solutions induced by the minimizer. Furthermore, we discuss to what extent such an application of the least action principle to subsolutions can serve as a selection criterion.
