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Research interests


Hamiltonian Partial differential equations

Birkhoff normal forms, KAM theorem, Long term behavior of Hamiltonian PDEs like Nonlinear Schrödinger equation, Nonlinear Klein Gordon equation, the Quantum Harmonic Oscillator in higher dimension

Nonlinear effects, beating phenomena in Hamiltonian PDEs

Modified scattering, resonant systems, asymptotic stability

Reducibility for linear time dependant Hamiltonian PDEs

Splitting methods for Hamiltonian PDEs

Variational methods for PDEs

Prepublications


  1. On reducibility of quantum harmonic oscillator on \R^d with quasiperiodic in time potential, B. Grébert, E. Paturel
    arXiv 35 p. (2016). Pdf



Publications and Works


  1. KAM for the Klein Gordon equation on \S^d, B. Grébert, E. Paturel
    Bollettino dell'Unione Matematica Italiana (BUMI) 9(2) 237--288 (2016). Pdf


  2. Modified scattering for the cubic Schrödinger equation on product spaces : the nonresonant case, B. Grébert, E. Paturel, L. Thomann
    Math. Research Letters 23 (3) 841--861 (2016). Pdf


  3. Beating effects in cubic Schrödinger systems and growth of Sobolev norms, B. Grébert, E. Paturel, L. Thomann
    Nonlinearity 26 1361--1376 (2013). Pdf


  4. Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part II: Abstract splitting., E. Faou, B. Grébert, E. Paturel
    Numerische Mathematik 114 (3) 459--490 (2010). Pdf


  5. Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part I. Finite-dimensional discretization, E. Faou, B. Grébert, E. Paturel
    Numerische Mathematik 114 (3) 429--458 (2010). Pdf


  6. Normal forms for semilinear quantum harmonic oscillators., B. Grébert, R. Imekraz, E. Paturel
    Communications in Mathematical Physics 291 (3) 763--798 (2009). Pdf


  7. Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems, J. Dolbeault, M. Loss, P. Felmer, E. Paturel
    Journal of Functional Analysis 238 (1) 193--220 (2005). Pdf


  8. Multiple homoclinic orbits for a class of Hamiltonian systems, E. Paturel
    Calc. Var. Partial Differential Equations 12 (2) 117--143 (2001). Pdf


  9. Solutions of Dirac-Fock equations without projector, E. Paturel
    Ann. Henri Poincaré 1 1123--1157 (2000). Pdf


  10. A new variational principle for a nonlinear Dirac equation on the Schwarzschild metric, E. Paturel
    Communications in Mathematical Physics 213 (2) 249--266 (2000). Pdf