Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916712209711104 |
|---|---|
| author | Jiao, Shuaijie Luo, Dejun |
| author_facet | Jiao, Shuaijie Luo, Dejun |
| contents | We investigate the inviscid 2D Boussinesq equations driven by rough transport noise of Kraichnan type with regularity index $α\in (0,1/2)$. For all $1<p<\infty$, 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 $0<α< 1-1/(p\wedge 2)$. The key ingredient is the anomalous regularity due to the noise proven by Coghi and Maurelli \cite{CogMau} who dealt with stochastic 2D Euler equations. Combining techniques from analysis and probability, we demonstrate how the additional regularity from noise compensates the singularity due to the nonlinear parts and coupled terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity Jiao, Shuaijie Luo, Dejun Probability Analysis of PDEs We investigate the inviscid 2D Boussinesq equations driven by rough transport noise of Kraichnan type with regularity index $α\in (0,1/2)$. For all $1<p<\infty$, 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 $0<α< 1-1/(p\wedge 2)$. The key ingredient is the anomalous regularity due to the noise proven by Coghi and Maurelli \cite{CogMau} who dealt with stochastic 2D Euler equations. Combining techniques from analysis and probability, we demonstrate how the additional regularity from noise compensates the singularity due to the nonlinear parts and coupled terms. |
| title | Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2504.19153 |