Well-posedness of the transport equation by stochastic perturbation
نویسندگان
چکیده
منابع مشابه
Well-posedness of the transport equation by stochastic perturbation
We consider the linear transport equation with a globally Hölder 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 partial differential equati...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2009
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-009-0224-4