Abstract
In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in Ref. 13. A solution theory for this equation has been developed recently in Ref. 27 based on regularity structure theory and paracontrolled distribution. In order to make the approximating equation converge to 3D NS equation driven by space-time white noise, we should subtract some drift terms in approximating equations. These drift terms, which come from renormalizations in the solution theory, converge to the solution multiplied by some constant depending on approximations.
| Original language | English |
|---|---|
| Article number | 1750020 |
| Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Dec 2017 |
Keywords
- Stochastic Navier-Stokes equation
- paracontrolled distribution
- regularity structure
- renormalization
- space-time white noise
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Zhu, R., & Zhu, X. (2017). Approximating 3D Navier-Stokes equations driven by space-time white noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 20(4), Article 1750020. https://doi.org/10.1142/S0219025717500205