The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier–Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier–Stokes equations in vorticity form; in particular, quantitative estimate allows us to choose the parameters of noise, uniformly in initial vorticity bounded in \(L^2\)-norm, so that global solutions exist with a large probability sufficiently close to 1.  

　　Publication:  

　　Journal of Dynamics and Differential Equations, 15 September 2023  

　　http://dx.doi.org/10.1007/s10884-023-10307  

　　Author:  

　　Dejun Luo  

　　Key Laboratory of RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China  

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China  

　　Email: luodj@amss.ac.cn