论文标题
关于随机3D Euler方程的耗散蛋白质解决方案的不良和良好性
On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
论文作者
论文摘要
我们关注的是随机三维不可压缩的欧拉方程的问题。特别是，我们介绍了一类新颖的耗散解决方案，并表明了（i）存在； （ii）虚弱的独特性； （iii）法律上的非唯一性； （iv）存在强大的马尔可夫解决方案； （v）强大的马尔可夫解决方案的非唯一性；在这个课程中所有这些都保持真实。此外，作为（iii）的副产品，我们获得了概率强的和分析性较弱的解决方案的存在和非唯一性，直到停止时间并满足能量不平等。
We are concerned with the question of well-posedness of stochastic three dimensional incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak--strong uniqueness; (iii) non-uniqueness in law; (iv) existence of a strong Markov solution; (v) non-uniqueness of strong Markov solutions; all hold true within this class. Moreover, as a byproduct of (iii) we obtain existence and non-uniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality.
