Dear all,

Here is the announcement of the next MAP seminar.

⟶ Thursday 6 March, at 11:30 in *Aula Riunioni* (if anyone requests, we can stream the event via google meet)

⟶ *Speaker**:* *Daniele Barbera* (Politecnico di Torino)

⟶ *Title**:* *The energy method applied to the existence of local and global solutions for liquid crystal models*

⟶ *Abstract**:* The energy method is a classical approach used to prove a priori estimates on parabolic PDEs. The equations we focus on are models for nematic liquid crystals: the Ericksen-Leslie and the Beris-Edwards model. These systems are based on a heat equation coupled with a Navier-Stokes equation. We will see how the energy method can be used to prove local and global solutions in time. In particular, we will consider N-dimensional exterior domains with initial conditions in Hs with s>N/2-1 for the Ericksen-Leslie model. For the Beris-Edwards model, instead, we will work on Rn with initial conditions in H1 .

We remind you that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

See you soon,

The organizers: Michele Caselli Francesco Malizia Jeremy Mirmina Filippo Paiano Leonardo Roveri

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