Pierre-Louis Lions

Collège de France Paris and CEREMADE, Université de Paris-Dauphine,France

Isabelle Gallagher

DMA, École normale supérieure, CNRS, PSL Research University Paris, FRANCE and Université de Paris.

Enrique Zuazua 

 Germany,Fundación Deusto, Bilbao,Universidad Autónoma de Madrid-Spain

14:00h – 14:40h

Numerics, Dynamics, Control and Machine Learning

In this lecture we shall present some of the work we have done and are developing in our team, with a special focus on the numerical analysis and computational aspects and paying special attention to the issues arising in the context of the control of dynamical systems and the emerging challenges in Machine Learning.

Yboon García,

Academic Department of Economics at the Universidad del Pacífico-Peru

Michel Duprez

14:00h – 14:40h

phi-FEM, A fictitious domain method for finite
element methods on domains defined by level-sets

Karine Beauchard

Univ Rennes, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France

Carlos Kenig

University of Chicago (USA)

Text14:00h – 14:40h

Channels of energy

We will discuss the role of non-radiative solutions to nonlinear wave equations, in connection with soliton resolution. Using new channels of energy estimates we characterize all radial non-radiative solutions for a general class of nonlinear wave equations. This is joint work with C.Collot, T. Duyckaerts and F. Merle. 

Francisco Gancedo

Universidad de Sevilla-Spain

14:50h – 15:30h

Global-in-time dynamics for one-phase Muskat and two-phase Stokes gravity waves

In this talk we consider the evolution of an interface
evolving by an incompressible flow. On the one hand, we study the
one-phase Muskat problem, where the fluid is filtered in a porous
medium. In the gravity-stable case, we show that initial Lipschitz
graphs of arbitrary size provide global-in-time well-posedness. On the
other hand, we study the interface dynamics given by two fluids of
different densities evolving by the linear Stokes law. We show stability
to the flat stable case and exponential growth in the unstable regime.

Enrique Fernandez Cara

Universidad de Sevilla (Spain)

14:00h – 14:40h

On the control of fluids

The Navier-Stokes equations have been studied since many years. They are very relevant in mathematics and physics and many people have been concerned with the solution of several related major open problems. On the other hand, the control of PDE’s has attracted a lot of work the last decades. This has been motivated by its very relevant role in applications. This talk is mainly devoted to present some recent results dealing with the local and global control of systems of the Navier-Stokes kind. Additionally, we will consider other equations and systems with origin in fluid mechanics.

Manuel A. Sanchez

Pontificia Universidad Católica de Chile (Chile)

Juan Luis Vazquez

Universidad Autónoma de Madrid Real
Academia de Ciências – Spain

Eduard Feireisl

Institute of Mathematics of the Academy of Sciences of the Czech Republic – Czech Republic

14:50h – 15:30h

Analysis of open fluid systems with uncertain data

We consider the Navier-Stokes-Fourier system with non-conservative boundary data. First, we discuss stability of (strong) solutions with respect to the data and conditional regularity problem. We show that the solutions remain regular as long as their amplitude is controlled. Next, we apply the abstract results to the problem of convergence of approximate (numerical) solutions with uncertain data. In particular, we address convergence of the stochastic collocation and the Monte-Carlo method.