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

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arxiv 2410.21855 v1 pith:G4TR4AKT submitted 2024-10-29 math.PR

Dejun Luo , Bin Xie , Guohuan Zhao This is my paper · ORCID
classification math.PR
keywords transportdataequationestimatesfullinitialnoisequantitative
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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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  1. A scaling limit for Vlasov equations with electrostatic fluctuations

    math.PR 2025-07 conditional novelty 6.0 of 10

    Random electrostatic fluctuations with fixed intensity and vanishing spatial correlation produce velocity diffusion in the Vlasov-Poisson limit, proving a deterministic Vlasov-Fokker-Planck equation.

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