论文标题
3D Euler方程的全球存在和非唯一性被运输噪声扰动
Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
论文作者
论文摘要
我们构建了Hölder连续的，全球概率上强的解决方案，以使Stratonovich运输噪声扰动3D Euler方程。可以将溶液的动能开处方，直到停止时间，可以以很高的概率任意选择。我们还证明，存在无限的Hölder连续初始条件，导致与系统相关的Cauchy问题的解决方案不唯一。我们的构建依赖于流动转化，将正在研究的SPDE降低为随机PDE，并在确定性环境中引入了De Lellis和SzékelyHidi在确定性环境中引入的凸积分技术，此处适合考虑使用随机情况。特别是，我们的新方法允许直接在$ [0，\ infty）$上构建概率强的解决方案。
We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Hölder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow transformation reducing the SPDE under investigation to a random PDE, and convex integration techniques introduced in the deterministic setting by De Lellis and Székelyhidi, here adapted to consider the stochastic case. In particular, our novel approach allows to construct probabilistically strong solutions on $[0,\infty)$ directly.
