论文标题
不可压缩欧拉方程的统计解决方案
Statistical solutions of the incompressible Euler equations
论文作者
论文摘要
我们在$ l^p $，$ 1 \ leq p \ leq \ infty $的两个维度上研究了不可压缩的欧拉方程的统计解决方案，在具有杰出标志的涡流表中。我们的统计解决方案概念是基于Bronzi，Mondaini和Rosa引起的框架。通过离散度量的近似值显示了这种环境中的存在，集中在Euler方程的确定性解决方案上。此外，我们提供的论点表明，可以在不可压缩的Navier-Stokes方程的统计解决方案的无关限制中获得Euler方程的统计解决方案。 Yudovich类显示了轨迹统计解决方案的独特性。
We study statistical solutions of the incompressible Euler equations in two dimensions with vorticity in $L^p$, $1\leq p \leq \infty$, and in the class of vortex-sheets with a distinguished sign. Our notion of statistical solution is based on the framework due to Bronzi, Mondaini and Rosa. Existence in this setting is shown by approximation with discrete measures, concentrated on deterministic solutions of the Euler equations. Additionally, we provide arguments to show that the statistical solutions of the Euler equations may be obtained in the inviscid limit of statistical solutions of the incompressible Navier-Stokes equations. Uniqueness of trajectory statistical solutions is shown in the Yudovich class.
