Mercoledì 17 novembre 2021
(Aula Fermi)
Scuola Normale Superiore
Pisa
Giorgio Stefani
(University of Basel)
terrà un seminario dal titolo:
"
An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces"
abstract:
We revisit Yudovich’s well-posedness result for the 2-dimensional
Euler equations for an inviscid incompressible fluid. Existence of
global-in-time weak solutions holds in suitable uniformly-localized
versions of the Lebesgue space and of the Yudovich space,
respectively, for the vorticity, with explicit modulus of continuity
for the associated velocity. Uniqueness of weak solutions, in
contrast to Yudovich’s energy method, follows from a Lagrangian
comparison. Our entire argument relies on elementary real-variable
techniques, with no use of either Sobolev spaces, Calderón-Zygmund
theory or Littlewood-Paley decomposition, and actually applies not
only to the Biot-Savart law, but also to more general operators
whose kernels obey some natural structural assumptions. This is a
joint work in collaboration with Gianluca Crippa.
il seminario si terrà in modalità mista.
Tutti gli interessati a partecipare in presenza devono contattare per email il dr. Gioacchino Antonelli (gioacchino.antonelli@sns.it).