Equazioni alle Derivate Parziali nella Dinamica dei Fluidi

# Lagrangian solutions of 2D Euler equations

speaker: Stefano Spirito (Università degli studi di L'Aquila)

abstract: Lagrangian Solutions of two dimensional Euler equations are, roughly speaking, solutions such that the vorticity is transported by the flow of the velocity. In this talk I will first give an overview regarding the existence of Lagrangian solutions and the equivalence between Lagrangian and Eulerian solutions. Then, I will discuss a recent result with Gianluca Crippa, Camilla Nobili, and Christian Seis concerning the convergence of Navier-Stokes solutions to Lagrangian solutions of the 2D Euler equations in the vanishing viscosity limit. A crucial tool in the proof of this result is a new uniqueness theorem for distributional solutions of linear continuity equations with vector fields whose gradient is a singular integral of an $$L^{1}$$ function.

timetable:
Tue 6 Feb, 16:10 - 16:45, Aula Dini
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