Volume 9, Issue 3
Global Existence of Axisymmetric Pathwise Solutions for Stochastic Three-Dimensional Axisymmetric Navier-Stokes Equations

Lihuai Du & Ting Zhang

East Asian J. Appl. Math., 9 (2019), pp. 447-464.

Published online: 2019-06

Preview Purchase PDF 22 5789
Export citation
  • Abstract

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.

  • Keywords

Stochastic Navier-Stokes equations, axisymmetric, global existence.

  • AMS Subject Headings

35Q35, 60H15, 76B03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-9-447, author = {}, title = {Global Existence of Axisymmetric Pathwise Solutions for Stochastic Three-Dimensional Axisymmetric Navier-Stokes Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {447--464}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.220418.210718}, url = {http://global-sci.org/intro/article_detail/eajam/13161.html} }
TY - JOUR T1 - Global Existence of Axisymmetric Pathwise Solutions for Stochastic Three-Dimensional Axisymmetric Navier-Stokes Equations 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 -

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.

Lihuai Du & Ting Zhang. (2019). Global Existence of Axisymmetric Pathwise Solutions for Stochastic Three-Dimensional Axisymmetric Navier-Stokes Equations. East Asian Journal on Applied Mathematics. 9 (3). 447-464. doi:10.4208/eajam.220418.210718
Copy to clipboard
The citation has been copied to your clipboard