论文标题
随机可压缩的欧拉方程和不可压缩极限的测量值解决方案
Measure-valued solutions to the stochastic compressible Euler equations and incompressible limits
论文作者
论文摘要
我们将耗散度量值的Martingale解决方案引入了随机压缩的Euler方程的新概念。这些解决方案在概率意义上是弱的，即概率空间和驾驶过程是解决方案不可或缺的一部分。我们得出了随机压缩欧拉方程的相对能量不等式，作为推论，我们表现出路线弱的独特原理。此外，利用相对能量不平等，我们研究了基础方程系统的低马赫极限（不可压缩极限）。作为相关文献的主要新颖性，我们的结果适用于Nemytskij类型的一般非线性乘数随机扰动。
We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.e., the probability space and the driving Wiener process are an integral part of the solution. We derive the relative energy inequality for the stochastic compressible Euler equations and, as a corollary, we exhibit pathwise weak-strong uniqueness principle. Moreover, making use of the relative energy inequality, we investigate the low Mach limit (incompressible limit) of the underlying system of equations. As a main novelty with respect to the related literature, our results apply to general nonlinear multiplicative stochastic perturbations of Nemytskij type.
