Global L_2-solutions of stochastic Navier-Stokes equations
| dc.creator | Mikulevicius, R. | |
| dc.creator | Rozovskii, B. L. | |
| dc.date | 2005-03-25 | |
| dc.date.accessioned | 2026-07-07T05:18:29Z | |
| dc.date.available | 2026-07-07T05:18:29Z | |
| dc.description | This paper concerns the Cauchy problem in R^d for the stochastic Navier-Stokes equation \partial_tu=Δu-(u,\nabla)u-\nabla p+f(u)+ [(σ,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad divu=0, driven by white noise \dot W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier-Stokes equations is established. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117904000000630 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0503597 | |
| dc.identifier | http://arxiv.org/abs/math/0503597 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 1, 137-176 | |
| dc.identifier | doi:10.1214/009117904000000630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74676 | |
| dc.subject | Probability | |
| dc.subject | 60H15, 35R60, 76M35 (Primary) | |
| dc.title | Global L_2-solutions of stochastic Navier-Stokes equations | |
| dc.type | text |