### Les mardis à 17h avec un thé dès 16h30

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## Exposés à venir :

22 octobre 2019
English
Anthony Royer (Université de Liège)
A valider

An optimized non-overlapping Schwarz method with cross-point treatment for high-frequency acoustic scattering problems
TBA
- Domain decomposition method (DDM),
- High-frequency acoustic modeling,
- Cross-points,
- Perfectly matched layer (PML)
29 octobre 2019
Toussaint Holidays (Sorbonne université)
Repos
5 novembre 2019
Pas de GTT / No GTT ( LJLL)
LIA COPDESC / Lions Magenes Days
Recouvrement avec : https://liacopdesclm.sciencesconf.org
12 novembre 2019
English
Bogdan Bulanyi (LJLL P7)
A valider

Regularity for the planar optimal p-compliance problem
To be modified

Given a bounded open set $\Omega \subset \mathbb{R}^{2}$, an exponent $p \in (1,+\infty)$ and a function $f \in L^{p^{\prime}}(\Omega)$ with $p^{\prime}=p/(p-1)$. We consider the problem
$(\mathcal{P}) \,\ \,\ \min\{C_{p}(\Sigma) + \lambda \mathcal{H}^{1}(\Sigma) : \Sigma \in \mathcal{K}(\Omega)\},$
where $\mathcal{K}(\Omega)$ is the class of compact connected subsets of the closure of $\Omega$, $\lambda>0$ is a fixed constant and $C_{p}$ is the $p$-compliance functional which for a given $\Sigma \in \mathcal{K}(\Omega)$ is defined as the maximum value of the functional
$u \mapsto \int_{\Omega} fu dx - \frac 1p \int_{\Omega \backslash \Sigma} |\nabla u|^{p} dx$ on the Sobolev space $W^{1,p}_{0}(\Omega \backslash \Sigma)$.

In this talk I will present a partial $C^{1,\alpha}$ regularity result, extending some of the results obtained by A. Chambolle, J. Lamboley, A. Lemenant and E. Stepanov (2017). I will prove that every solution of problem $(\mathcal{P})$ has no loops (i.e. homeomorphic images of $S^{1}$), is Ahlfors-regular, and $C^{1,\alpha}$-regular at $\mathcal{H}^{1}$-a.e. point for every $p \in (1,+\infty)$.
26 novembre 2019
Julia Delacour (LJLL/INRIA/Vienna )
A valider

Biology, dynamical system, transport-coagulation equation (temporary title)
TBA
3 décembre 2019
Gabriela Lopez Ruiz (LJLL)
A valider

Ocean boundary layer formation: the quasi-geostrophic model
We will talk about the the impact of small-scale irregularities on the coasts on oceanic circulation at the mesoscale. The classical quasi-geostrophic model is considered as the starting point in this analysis of coastal boundary layer formation. Boundary layer theory addresses well the dynamics of ocean currents since the observation of long-wavelength ocean waves within several days has shown that friction forces are negligible compared to other forces involved (pressure, Coriolis force, etc). The western boundary layer plays a fundamental role in basin-scale wind-driven ocean circulations and it has been long emphasised in several theoretical works. In idealised ocean models with flat bottom topography, this layer is required not only to balance the interior Sverdrup transport to close the gyre circulation, but also to dissipate the vorticity imposed by the wind-stress curl. Thus, we will focus our attention in the well-posedness of the western boundary layer problem in this regime.

## Exposés passés :

Liste des exposés passés

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### Le séminaire a lieu sur le site de Jussieu:

4 Place Jussieu 75005 Paris
Salle des séminaires au 3ème étage, couloir 15-16
Accès : et , station Jussieu.

Pour tout renseignement sur le GTT, contacter: Jules Pertinand (pertinand@ljll.math.upmc.fr), Gabriela López Ruiz (lopez-ruiz@ljll.math.upmc.fr)