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Article Dans Une Revue Inventiones Mathematicae Année : 2010

Well-posedness of the transport equation by stochastic perturbation

Résumé

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.

Dates et versions

hal-00359723 , version 1 (09-02-2009)

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Franco Flandoli, Massimiliano Gubinelli, Enrico Priola. Well-posedness of the transport equation by stochastic perturbation. Inventiones Mathematicae, 2010, 180 (1), pp.1-53. ⟨10.1007/s00222-009-0224-4⟩. ⟨hal-00359723⟩
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