We investigate the inviscid 2D Boussinesq equations driven by rough transport noise of Kraichnan type with regularity index α ∈ (0, 1/2). For all 1 < p < ∞, we establish the existence and uniqueness of probabilistic strong solutions for all L^p initial vorticity and L^2 initial temperature, under the parameter constraint 0 < α < 1 - 1/(p ∧ 2). Based on the noise-induced anomalous regularity established by Coghi and Maurelli, we show that the stochastic Boussinesq system is stable with respect to the initial data, which not only implies the pathwise uniqueness, but also enables us to directly prove existence of probabilistically strong solutions without resorting to the compactness method.

Publication:

MATHEMATISCHE ANNALEN

http://dx.doi.org/10.1007/s00208-026-03555-w

Author:

Shuaijie Jiao

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

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

jiaoshuaijie@amss.ac.cn

Dejun Luo

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

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

luodj@amss.ac.cn