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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Well-posedness of the transport equation by stochastic perturbation

## Well-posedness of the transport equation by stochastic perturbationAdd to your list(s) Download to your calendar using vCal - Priola, E (Turin)
- Thursday 01 April 2010, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Stochastic Partial Differential Equations (SPDEs) This is a joint work with F. Flandoli and M. Gubinelli. We consider the linear transport equation with a globally H”{o}lder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the deterministic PDE , 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 a PDE of fluid dynamics that becomes well-posed under the influence of a (multiplicative) noise. The key tool is a differentiable stochastic flow constructed and analyzed by means of a special transformation of the drift of It^{o}-Tanaka type. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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