Well-posedness of the transport equation by stochastic perturbation
type: Item
instance of: scholarly article
title: Well-posedness of the transport equation by stochastic perturbation
zbMATH Open document ID: 1200.35226
author: Massimiliano Gubinelli
author: Franco Flandoli
author: E. Priola
published in: Inventiones Mathematicae
publication date: 2010-03-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/0809.1310
review text: It is known at the moment that the linear transport equation in hydrodynamics may have multiple solutions of a Cauchy problem in some functional spaces. The main ideological result of the paper under consideration is that under a suitable random perturbation the \(L^\infty\) solutions are unique even in the case where the Cauchy problem for the unperturbed deterministic equation has multiple solutions. This result is obtained by introducing a special multiplicative white noise into the PDE. The assumption on the PDE is that the vector filed is globally Hölder continuous and bounded and satisfies the integrability condition for its divergence.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 5677792
zbMATH Keywords: Transport equation
zbMATH Keywords: stochastic perturbation
zbMATH Keywords: existence and uniqueness of solutions
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
OpenAlex ID: W2055459591
arXiv ID: 0809.1310
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DOI: 10.1007/S00222-009-0224-4
description: scientific article