# Transport equations with coefficient having a gradient given by a singular integral, and applications

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FranĂ§ois Bouchut
(Ecole Normale SupĂ©rieure)

created by magnani on 05 May 2008

14 may 2008

**Abstract.**

I shall talk about a recent work in collaboration with G. Crippa in which we prove that a linear transport equation with unsmooth coefficient is well-posed, in the sense of existence and uniqueness of a generalized flow, when the coefficient has first-order derivatives given by singular integrals of L^{1} functions. This regularity is not comparable to the case of coefficient in BV, and has applications in two-dimensional Euler equations, and arbitrary dimensional
Vlasov-Poisson system.