IPSO - 2011 - Annual activity report

IPSO

IPSO - 2011

Project Team Ipso

Members

Overall Objectives

An overview of geometric numerical integration
Overall objectives
Highlights

Scientific Foundations

Structure-preserving numerical schemes for solving ordinary differential equations
Highly-oscillatory systems
Geometric schemes for the Schrödinger equation
High-frequency limit of the Helmholtz equation
From the Schrödinger equation to Boltzmann-like equations
Spatial approximation for solving ODEs

Application Domains

Laser physics
Molecular Dynamics

New Results

Asymptotic preserving schemes
Resolution of the quasi-neutrality equation
High order schemes for Vlasov-Poisson system
Second order averaging for the nonlinear Schrödinger equation with strong anisotropic potential
A problem of moment realizability in quantum statistical physics
Orbital stability of spherical galactic models
The Schrödinger Poisson system on the sphere
A boundary matching micro-macro decomposition for kinetic equations
1D quintic nonlinear equation with white noise dispersion
Weak approximation of stochastic partial differential equations: the nonlinear case
Ergodic BSDEs under weak dissipative assumptions
Asymptotic first exit times of the Chafee-Infante equation with small heavy tailed noise
Stochastic Cahn-Hilliard equation with double singular nonlinearities and two reflections
Diffusion limit for a stochastic kinetic problem
Convergence of stochastic gene networks to hybrid piecewise deterministic processes
Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noise
Ergodicity results for the stochastic Navier-Stokes equations: an introduction
Local Martingale and Pathwise Solutions for an Abstract Fluids Model
Geometric numerical integration and Schrödinger equations
On the influence of the geometry on skin effect in electromagnetism
Reconciling alternate methods for the determination of charge distributions: A probabilistic approach to high-dimensional least-squares approximations
Hamiltonian interpolation of splitting approximations for nonlinear PDEs
Energy cascades for NLS on the torus
A Nekhoroshev type theorem for the nonlinear Schrödinger equation on the d-dimensional torus
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus
Approximate travelling wave solutions to the 2D Euler equation on the torus
Markov chains competing for transitions : applications to large-scale distributed systems
Analysis of a large number of Markov chains competing for transitions
Splitting methods with complex coefficients for some classes of evolution equations
Higher-order averaging, formal series and numerical integration

Contracts and Grants with Industry

Contracts with Industry

Partnerships and Cooperations

National Initiatives
European Initiatives
International Initiatives

Dissemination

Animation of the scientific community
Teaching

Bibliography

Major publications
Publications of the year
References in notes

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Section: New Results

Ergodicity results for the stochastic Navier-Stokes equations: an introduction

Participant : Arnaud Debussche.

In thus survey article [46] , we review recent progresses in the study of ergodicity for the stochastic Navier-Stokes equations. The first part introduces general concept, the second deals with the 2D case and the 3D case is treated in the third part.

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