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Mardi 10 Octobre
| Heure: |
13:30 - 14:30 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
PM - EDP - Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations - |
| Description: |
Mihaela IfrimWe provide a complete local well-posedness theory in $H^s$
based Sobolev spaces for the free boundary incompressible Euler
equations with zero surface tension on a connected fluid domain.
Our well-posedness theory includes: (i) Local well-posedness in
the Hadamard sense, i.e., local existence, uniqueness, and the
first proof of continuous dependence on the data, all in low
regularity Sobolev spaces; (ii) Enhanced uniqueness: Our
uniqueness result holds at the level of the Lipschitz norm of
the velocity and the $C^{1,frac{1}{2}}$ regularity of the free
surface; (iii) Stability bounds:  We construct a nonlinear
functional which measures, in a suitable sense, the distance
between two solutions (even when defined on different domains)
and we show that this distance is propagated by the flow; (iv)
Energy estimates: We prove refined, essentially scale invariant
energy estimates for solutions,  relying on   a newly
constructed family of elliptic estimates; (v) Continuation
criterion: We give the first proof of a sharp continuation
criterion in the physically relevant pointwise norms, at the
level of scaling. In essence, we show that solutions can be
continued as long as the velocity is in $L_T^1W^{1,infty}$ and
the free surface is in $L_T^1C^{1,frac{1}{2}}$, which is at the
same level as the Beale-Kato-Majda criterion for the
boundaryless case; (vi) A  novel proof of the construction of
regular solutions.
 
 Our entire approach is in the Eulerian framework and can be
adapted to work in more general fluid domains.  |
Mercredi 11 Octobre
| Heure: |
13:30 - 16:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Théorie Ergodique et Systèmes Dynamiques - Normal numbers with constraints - |
| Description: |
Olivier Carton
We first recall the definition of normality which is a kind of (very) We consider normal number digit dependencies in their We quantify precisely how much digit dormal.  real numbers are absolutely normal. |
| Heure: |
13:30 - 16:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Théorie Ergodique et Systèmes Dynamiques - Perfect necklaces - |
| Description: |
Verónica Becher
A necklace is a circular word over a finite alphabet. A necklace is (n,k)?perfect if each word of length n occurs exactly k times, at We present different families of perfect The discrete discrepancy  of a  necklace is  function that  indicates how far away the segments For some perfect necklaces their exact discrepancy is known. These  perfect necklaces are used  |
Jeudi 12 Octobre
| Heure: |
10:15 - 12:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Topologie algébrique - Corecognition for iterated suspensions - |
| Description: |
Oisín Flynn-Connolly |
Vendredi 13 Octobre
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Géométrie Arithmétique et Motivique - Pas d'exposé - |
| Description: |
Conférence en l'honneur de Jan Nekovar à l'IHES |
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