论文标题
Martingale解决方案的全球存在对随机可压缩的Navier-Stokes方程的密度依赖性粘度
The Global Existence of Martingale Solutions to Stochastic Compressible Navier-Stokes Equations with Density-dependent Viscosity
论文作者
论文摘要
本文确定了由随机外部力驱动的可压缩的Navier-Stokes方程，具有密度依赖性粘度和真空的全球存在。这项工作可以被视为确定性的Navier-Stokes方程的随机版本\ cite {vasseur-yu2016}（vasseur-yu，发明，发明数学，206：935---974，2016。），其中全球较弱的解决方案的存在是为弱化的解决方案而建立的，用于绝经eppectonement oppectement $γ$γ> 1 $ 1 $。对于随机情况，以非线性术语的限制，密度和速度的规律性甚至更糟。我们设计一个正规系统以近似原始系统。为了弥补缺乏速度的规律性，我们还需要在\ cite {vasseur-yu-q2016，vasseur-yu2016}中添加一个人工雷利阻尼术语。此外，我们必须按不同的顺序将人工条款发送至$ 0 $。
The global existence of martingale solutions to the compressible Navier-Stokes equations driven by stochastic external forces, with density-dependent viscosity and vacuum, is established in this paper. This work can be regarded as a stochastic version of the deterministic Navier-Stokes equations \cite{Vasseur-Yu2016} (Vasseur-Yu, Invent. Math., 206:935--974, 2016.), in which the global existence of weak solutions was established for adiabatic exponent $γ> 1$. For the stochastic case, the regularity of density and velocity is even worse for passing the limit in nonlinear terms. We design a regularized system to approximate the original system. To make up for the lack of regularity of velocity, we need to add an artificial Rayleigh damping term besides the artificial viscosity and damping forces in \cite{Vasseur-Yu-q2016,Vasseur-Yu2016}. Moreover, we have to send the artificial terms to $0$ in a different order.
