论文标题
3D随机Navier-Stokes方程的局部强解决方案的时空近似
Space-time approximation of local strong solutions to the 3D stochastic Navier-Stokes equations
论文作者
论文摘要
我们考虑了圆环上的3D随机Navier-Stokes方程。我们的主要结果涉及局部强路解决方案的时间和时空离散。我们证明，对于概率收敛性的能量误差，我们证明了最佳的收敛速率，即及时的空间和顺序（最高）1/2的顺序收敛。该结果可以实现（时滴）解决方案的可能爆炸。我们的方法基于（时间差异）解决方案的离散停止时间。
We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with respect to convergence in probability, that is convergence of order 1 in space and of order (up to) 1/2 in time. The result holds up to the possible blow-up of the (time-discrete) solution. Our approach is based on discrete stopping times for the (time-discrete) solution.
