Calculus of Variations and Geometric Measure Theory
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Transport equations with coefficient having a gradient given by a singular integral, and applications

François Bouchut (Ecole Normale Supérieure)

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 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.

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