For the stochastic linear transport equation with L-p-initial data (1 < p < 2) on the full space \BbbRd, we provide quantitative estimates, in negative Sobolev norms, between its solutions and those of the deterministic heat equation. Moreover, for initial data in L-p with p is an element of (root 2, 2), we establish a similar estimate between the solutions of stochastic 2D Euler equations and deterministic 2D Navier-Stokes equation in vorticity form.

Publication:

SIAM JOURNAL ON MATHEMATICAL ANALYSIS

http://dx.doi.org/10.1137/24M1706815

Author:

DEJUN LUO

SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences,Beijing 100049, China

luodj@amss.ac.cn

BIN XIE

Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto, Nagano 390-8621, Japan

bxie@shinshu-u.ac.jp

GUOHUAN ZHAO

SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China

gzhao@amss.ac.cn