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arXiv · 2410.21855

Quantitative estimates for SPDEs on the full space with transport noise and $L^p$-initial data

Dejun Luo·Bin Xie·Guohuan Zhao
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Abstract

For the stochastic linear transport equation with $L^p$-initial data ($1<p<2$) on the full space $\mathbb{R}^d$, we provide quantitative estimates, in negative Sobolev norms, between its solutions and that of the deterministic heat equation. Similar results are proved for the stochastic 2D Euler equations with transport noise.

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Dejun Luo, Bin Xie, Guohuan Zhao. 2024-10-29. Quantitative estimates for SPDEs on the full space with transport noise and $L^p$-initial data. https://arxiv.org/abs/2410.21855

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