On the convergence of stochastic transport equations to a deterministic parabolic one

Lucio Galeati

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arXiv · 1902.06960

On the convergence of stochastic transport equations to a deterministic parabolic one

Lucio Galeati

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Abstract

A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension $d\geq 2$; the case $d=1$ is also investigated but no conclusive answer is obtained.

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Lucio Galeati. 2019-02-19. On the convergence of stochastic transport equations to a deterministic parabolic one. https://arxiv.org/abs/1902.06960

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