TY - JOUR
T1 - Global Existence of Axisymmetric Pathwise Solutions for Stochastic Three-Dimensional Axisymmetric Navier-Stokes Equations
AU - Lihuai Du & Ting Zhang
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 447
EP - 464
PY - 2019
DA - 2019/06
SN - 9
DO - http://doi.org/10.4208/eajam.220418.210718
UR - https://global-sci.org/intro/article_detail/eajam/13161.html
KW - Stochastic Navier-Stokes equations, axisymmetric, global existence.
AB - <p style="text-align: justify;">A stochastic three-dimensional Navier-Stokes system with the axisymmetric
initial data and white noise is studied. It is shown that if the swirl component of the
initial velocity field and the white noise are sufficiently small, then the axisymmetric
pathwise solution is global in probability. Moreover, in the absence of the swirl, the
pathwise axisymmetric solution is global almost surely.</p>