The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.

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# Year 2020

**Friday 26th June 2020 at 14h
**
Kathrin Stollenwerk
(Aachen University),
*à venir*

**Friday 21st February 2020 at 14h
**
Rémi Abgrall
(Univ Zürich, IMCS),
*SUPPRIMER Nouvelle date à venir*

**Friday 31st January 2020 at 14h
**
Marco Picasso
(EPFL, Laussane),
*Eléments finis anisotropes*

**Friday 17th January 2020 at 15h
**
Stefano Spirito
(Gran Sasso Science Institute, Italy),
*Weak solutions of the 2D Euler equations*

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In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.

**Friday 17th January 2020 at 14h
**
Paolo Antonelli
(Gran Sasso Science Institute, Italy),
*An intrinsically hydrodynamic approach to one dimensional quantum hydrodynamic systems*

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Quantum hydrodynamic (QHD) systems arise in the effective description of phenomena where quantistic behavior can be seen also at a macroscopic scale. This is the case for instance in Bose-Einstein condensation, superfluidity or in the modeling of semiconductor devices. Standard results for global existence of finite energy weak solutions to the QHD system often exploit the analogy with a nonlinear Schrödinger equation; by using the Madelung transform it is possible to define a solution to the QHD by considering the momenta (mass and current density) associated to a wave function. In particular this argument requires the initial data to be determined by a given wave function. This usual approach hence shows the existence of solutions but can not be used to study their stability properties in a general framework. In this talk I will present some recent developments that overcome those difficulties for the one dimensional QHD system. First of all I will provide an existence result for a large class of initial data, without requiring them to be generated by a wave function. Furthermore, I will prove a stability result for weak solutions. This exploits a novel functional which formally controls the L^2 norm of the chemical potential, weighted with the particle density. This is a joint work with P. Marcati and H. Zheng.

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.

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Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
all years together.