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Szeftel, Jeremie (UMPC Paris)  WPI, OMP 1, Seminar Room 08.135  Mon, 23. Oct 17, 14:00 
The nonlinear stability of Schwarzschild  
I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class.  

Vega, Luis (BCA Bilbao)  WPI, OMP 1, Seminar Room 08.135  Mon, 23. Oct 17, 15:30 
Selfsimilar solutions of the Binormal Flow: a new approach  
I shall present some recent results obtained with F. de la Hoz about the selfsimilar solutions of the Binormal Flow, also known as the Vortex Filament Equation. Some connections with the transfer of energy in the case when the filament is a regular polygon will be also made.  

Visciglia, Nicola (U.Pisa)  WPI, OMP 1, Seminar Room 08.135  Mon, 23. Oct 17, 16:30 
Large data scattering for gKdV  
By combining the KenigMerle approach with a suitable inequality proved by Tao we deduce that solutions to gKdV, in the L^2supercitical regime, scatter to free waves for large times.  

Lenzman, Enno (U.Basel)  WPI, OMP 1, Seminar Room 08.135  Tue, 24. Oct 17, 9:00 
EnergyCritical HalfWave Maps: Solitons and Lax Pair Structure  
We discuss some essential features of solitons for the energycritical halfwave maps equation. Furthermore, we will present a Lax pair structure and explain its applications to understanding the dynamics. The talk is based on joint work with P. Gérard (Orsay) and A. Schikorra (Pittsburgh).  

Munoz, Claudio (U. Chile Santiago)  WPI, OMP 1, Seminar Room 08.135  Tue, 24. Oct 17, 10:30 
Local decay estimates for nonlinear equations in the energy space  
In this talk we will discuss some recent improvements on wellknown decay estimates for nonlinear dispersive and wave equations in 1D with supercritical decay, or no decay at all. Using Virial estimates, we will get local decay where standard dispersive techniques are not available yet. These are joint works with M.A. Alejo, M. Kowalczyk, Y. Martel, F. Poblete, and J.C. Pozo.  

Merle, Frank (IHES & U. Cergy Pontoise)  WPI, OMP 1, Seminar Room 08.135  Tue, 24. Oct 17, 15:00 
Different notion of nondispersive solutions for hyperbolic problems  
We will see various notion of nondispersive solution in the case of the energy criticl wave equation and applications.  

Lan, Yang (U.Basel)  WPI, OMP 1, Seminar Room 08.135  Tue, 24. Oct 17, 16:30 
On asymptotic dynamics for $L^2$critical gKdV with saturated perturbations  
We consider the $L^2$ critical gKdV equation with a saturated perturbation. In this case, all $H^1$ solution are global in time. Our goal is to classify the asymptotic dynamics for solutions with initial data near the ground state. Together with a suitable decay assumption, there are only three possibilities: (i) the solution converges asymptotically to a solitary wave, whose $H^1$ norm is of size $gamma^{2/(q1)}$, as $gammarightarrow0$; (ii) the solution is always in a small neighborhood of the modulated family of solitary waves, but blows down at $+infty$; (iii) the solution leaves any small neighborhood of the modulated family of the solitary waves. This extends the result of classification of the rigidity dynamics near the ground state for the unperturbed $L^2$ critical gKdV (corresponding to $gamma=0$) by Martel, Merle and Rapha"el. It also provides a way to consider the continuation properties after blowup time for $L^2$ crtitical gKdV equations.  

Zaag, Hatem (U.Paris 13)  WPI, OMP 1, Seminar Room 08.135  Wed, 25. Oct 17, 9:00 
Blowup solutions for two nonvariational semilinear parabolic systems  
We consider two nonvariational semilinear parabolic systems, with different diffusion constants between the two components. The reaction terms are of power type in the first system. They are of exponential type in the second. Using a formal approach, we derive blowup profiles for those systems. Then, linearizing around those profiles, we give the rigorous proof, which relies on the twostep classical method: (i) the reduction of the problem to a finitedimensional one, then, (ii) the proof of the latter thanks to Brouwer's lemma. In comparison with the standard semilinear heat equation, several technical problems arise here, and new ideas are needed to overcome them. This is a joint work with T. Ghoul and V.T. Nguyen from NYU Abu Dhabi.  

Collot, Charles (U.Nice)  WPI, OMP 1, Seminar Room 08.135  Wed, 25. Oct 17, 10:30 
Shock formation for Burgers equation with transversal viscosity  
This talk is about singularity formation for solutions to $$ (*) partial_{t}u+upa_x upa_{yy}u=0, (x,y) in mathbb R^2 $$ which is a simplified model of Prandtl's boundary layer equation. Note that it reduces to Burgers equation for $y$independent solutions $u(t,x,y)=v(t,x)$. We will first recast the wellknown shock formation theory for Burgers equation using the framework of selfsimilar blowup. This will provide us with an analytic framework to study the effect of the transversal viscosity. The main result (still work in progress) is the construction and precise description of singular solutions to $(*)$. This is joint work with T.E. Ghoul and N. Masmoudi.  

Banica, Valeria (U.Evry)  WPI, OMP 1, Seminar Room 08.135  Wed, 25. Oct 17, 15:00 
1D cubic NLS with several Diracs as initial data and consequences  
We solve the cubic nonlinear Schrödinger equation on $mathbb R$ with initial data a sum of Diracs. Then we describe some consequences for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3D fluids and superfluids. This is a joint work with Luis Vega.  

Ivanovici, Oana (CNRS Nice)  WPI, OMP 1, Seminar Room 08.135  Wed, 25. Oct 17, 16:30 
Dispersion estimates for the wave equation outside a strictly convex obstacle in 3D  
We consider the linear wave equation outside a compact, strictly convex obstacle in R^3 with smooth boundary and we show that the linear wave flow satisfies the dispersive estimates as in R^3 (which is not necessarily the case in higher dimensions).  

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