Well-posedness of the transport equation by stochastic perturbation
Flandoli, Franco; Gubinelli, Massimiliano; Priola, Enrico (2010), Well-posedness of the transport equation by stochastic perturbation, Inventiones Mathematicae, 180, 1, p. 1-53. http://dx.doi.org/10.1007/s00222-009-0224-4
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00359723/en/
Journal nameInventiones Mathematicae
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Abstract (EN)We consider the linear transport equation with a globally Holder continuous and bounded vector field. While this deterministic PDE may not be well-posed, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of partial differential equation that become well-posed under the influece of noise. The key tool is a differentiable stochastic flow constructed and analysed by means of a special transformation of the drift of Tanaka type.
Subjects / KeywordsProbability
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Priola, Enrico; Gubinelli, Massimiliano; Flandoli, Franco (2011) Article accepté pour publication ou publié
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