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 L¹ 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.