[Dottorcomp] Seminari di Matematica Applicata, 04/02/2025, Gianluca Crippa

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 4 Febbraio 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Gianluca Crippa (Università di Basilea)
terrà un seminario dal titolo:

Weak, renormalized, and vanishing-viscosity solutions of the
two-dimensional Euler equations.

Abstract.
Let us consider the Euler equations modeling the behavior of an
incompressible, homogeneous, inviscid fluid. In the two-dimensional case,
the Euler equations can be written in vorticity form as a continuity
equation, in which the advecting velocity depends on the vorticity through
an integral operator. In my talk, I will introduce several notions of weak
solutions for the two-dimensional Euler equations in vorticity form: weak
solutions, renormalized solutions, and vanishing-viscosity solutions.
Relying on the linear theory for continuity equations with Sobolev velocity
field by DiPerna and Lions, I will show that in the subcritical case weak
solutions do not exhibit anomalies. In the supercritical case, I will show
by means of a duality approach that the same holds for vanishing-viscosity
solutions. This has some connections with the two-dimensional theory of
turbulence of Kraichnan and Batchelor.
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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/