Programme
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mardi 9 juin 2026 |
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09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
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›9:30 (40min)
Thomas Alazard
Title: A fluid-structure problem with free surface. Abstract: We consider a fluid-structure problem governed by the incompressible Euler equations with a free surface, in a domain whose interface is governed by linear elasticity. Our main result asserts that the Cauchy problem is globally well-posed in time for any irrotational initial data in the energy space, without smallness assumption. In the absence of parabolic regularization, we prove that the system may be reformulated as a nonlinear Schrödinger-type equation. This enables the construction of solutions that are highly irregular from the perspective of inviscid fluid dynamics: the initial fluid velocity possesses merely half a derivative in L2. Joint work with Chengyang Shao (IHES) and Haocheng Yang (NYU Abu Dhabi).
›10:20 (40min)
Claude Zuily
Unique continuation for fractional powers oh sub-elliptic operators
›11:30 (40min)
Sebastian Herr
Title: The cubic Dirac equation and its non-relativistic limit. Abstract: A scale-invariant global well-posedness and scattering theory for cubic Dirac equations will be presented. It is based on a modular approach using critical adapted function spaces and bilinear Fourier restriction theory. As an application, we can study the non-relativistic limit, more precisely, convergence towards a system of cubic nonlinear Schrödinger equations. This is joint work with Timothy Candy.
›15:00 (40min)
Jérôme Le Rousseau
Title: Observation of the Stokes system under general boundary conditions. Abstract. Near a boundary, we recast the Stokes system as a first-order system. A microlocal matrix reduction then makes it possible to derive a Carleman estimate. Because of the presence of Jordan blocks, this estimate exhibits a loss of a full derivative, which makes its derivation delicate, in particular when patching together microlocal estimates. The boundary estimate can then be used to obtain an observability estimate for the Stokes or Oseen system, the latter being a linearization of the Navier–Stokes system. Controllability results can then be deduced. General boundary conditions are considered, in the spirit of the Lopatinskii–Shapiro conditions, including the classical Dirichlet, Navier, and Neumann conditions. This joint work with Luc Robbiano.
›15:50 (40min)
Belhassen Dehman
Title: Regional and partial observability and control of waves. Abstract: We establish sharp regional observability results for solutions of the wave equation in a bounded domain Ω of R^n. Given a non-empty open subset ω ⊂ Ω, we derive estimates for the energy of initial data supported in another open subset O ⊂ Ω, in terms of the energy measured on the observation set (0,T )×ω. This holds under a suitable geometric condition relating the time horizon T and the pair of subdomains (ω,O), which is weaker than the so-called Geometric Control Condition (GCC). A notable feature of our approach is that it remains effective in settings where classical unique continuation results doesn’t apply. The proof combines a high-frequency observability estimate — based on the propagation of singularities — with a compactness-uniqueness argument that exploits the unique continuation properties of elliptic operators. By duality, this observability result leads to regional controllability results.
›17:00 (40min)
Gigliola Staffilani
Title: Some mathematically rigorous results in wave turbulence theory. Abstract: In this talk we give an overview of some old and new mathematical advances in wave turbulence theory. We start with the original perspective of Bourgain on the study of the energy spectrum for a periodic nonlinear Schrödinger equation via growth of Sobolev norms. Then we move to the wave kinetic equations as effective equations for the energy spectrum and we give examples of rigorous proofs of condensate growth and energy transfer.
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Discours/Intervention |
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Logistique |
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