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Home > Research teams

Analysis, Partial Differential Equations

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The main research themes of the team are the following:

  • Analysis of kinetic and fluid mechanics equations
  • Elliptic equations, Analysis on manifolds
  • Riemannian geometry. Functional inequalities and Optimal transport
  • Functional and Harmonic Analysis, Operator theory and algebras
  • Quantum Probability and Mechanics
  • Optimal control and regularity in variational calculus, topological methods.

Detailed Presentation

Surface de niveau de la norme d'un champ de vecteurs de divergence nulle ayant certaines symétries

  • Analysis of kinetic and fluid mechanics equations

Applications of functional spaces to PDEs. Qualitative properties of solutions (stability, asymptotic behavior, etc.). Boltzmann, Navier-Stokes and Euler equations. Non-Newtonian fluids, fluids in rotation, capillarity problems. Kinetic theories with and without collisions. Applications of harmonic analysis to PDEs. Approximation of incompressible flows with weakly compressible flows. Shallow water wave equations and formation of singularities.

  • Elliptic equations, Analysis on manifolds

Qualitative properties of solutions of nonlinear elliptic PDEs. Stability and instability. Study of the 3D Ginzburg-Landau equation: structure of the natural boundary data, asymptotic behavior of the energy. Questions in functional analysis (Sobolev spaces between manifolds, general theory of degree). Minimal surfaces and stationary varifolds. Classification of singularities, global regularity, calibrations.

  • Riemannian geometry. Functional inequalities and convergence to equilibrium. Optimal transport

Studying geometric and functional inequalities (such as Poincaré and logarithmic Sobolev inequalities), we analyze the asymptotic behavior of diffusion equations, such as Fokker-Planck or Ornstein-Uhlenbeck equations. Optimal transport and Ricci curvature. Regularity questions in optimal transport.

  • Functional and Harmonic Analysis, Operator theory and algebras

We combine methods from complex analysis, functional analysis, harmonic analysis and of Banach spaces geometry, to study questions from interpolation theory, operator theory, reproducing kernels, approximation, etc.

  • Quantum Probability and Mechanics

Quantum noise, mechanics, statistical mechanics, stochastic calculus and random walks.

  • Optimization. Optimal control and regularity in variational calculus, topological methods

The main directions are: geometric measure theory; necessary optimality conditions in optimizations; Hamilton-Jacobi equations in control theory; construction of state feedbacks in optimal and stabilizing control; Hilbert-Haar theory in calculus of variations. Variational inequalities and applications to the stability of stationary solutions. Coercivity properties of non smooth functionals. Differential inclusions. Use of the theory of asymptotic functions for optimization and for variational inequalities (new penalty and barrier methods, new techniques for the convergence analysis); new optimization algorithms, based on non-euclidian projections which take constraints into account. Hyperbolic problems with low regularity coefficients: well-posedness and control.



 Simon Andreys   +33 (0)472431189   (UCBL-Braconnier  111B)    
 Stéphane Attal   +33 (0)472431253   (UCBL-Braconnier  208)    
 Nadine Badr   +33 (0)472431077   (UCBL-Braconnier  209)    
 Ivan Bardet   +33 (0)472431189   (UCBL-Braconnier  111B)    
 Pierre Bochard   +33 (0)472431260   (UCBL-Braconnier  224)    
 Lorenzo Brandolese   +33 (0)472447939   (UCBL-Braconnier  238)    
 Valentina Busuioc   +33 (0)477481552   (UJM-Metare  C104)    
 Gilles Cassier   +33 (0)472446270   (UCBL-Braconnier  216)    
 Benjamin Celaries   +33 (0)472431189   (UCBL-Braconnier  111B)    
 Francis Clarke   +33 (0)472448258   (UCBL-Braconnier  204)    
 Olivier Druet   +33 (0)472431149   (UCBL-Braconnier  109A)    
 Louis Dupaigne   +33 (0)426234554   (UCBL-Braconnier  126)    
 Francesco Fanelli   +33 (0)472447949   (UCBL-Braconnier  258)    
 Ivan Gentil   +33 (0)472448578   (UCBL-Braconnier  102)    
 Rafael Granero Belinchon   +33 (0)472431260   (UCBL-Braconnier  224)    
 Jiao He   +33 (0)472431689   (UCBL-Braconnier  111A)    
 Chih-Kang Huang   +33 (0)426234513   (UCBL-Braconnier  109E)    
 Dragos Iftimie   +33 (0)472447958   (UCBL-Braconnier  232)    
 Petru Mironescu   +33 (0)472448113   (UCBL-Braconnier  210)    
 Luigia Ripani   +33 (0)472431076   (UCBL-Braconnier  101 bis)    
 Maria Caterina Vâlcu   +33 (0)472446219   (UCBL-Braconnier  243)    
 Cédric Villani   +33 (0)144276792   (UCBL-Braconnier  004)    
 Simon Zugmeyer   +33 (0)426234513   (UCBL-Braconnier  109E)    

Nombre de personnes : 23