Préprints

E. Faou, F. Rousset, T. Seetohul, Large time nonlinear dynamics close to inhomogeneous stationary states of the Vlasov-HMF model, arxiv

D. Han-Kwan, F. Rousset,  Semiclassical limit of cubic nonlinear Schrödinger equations for mixed states, arxiv

F. Rousset, C. Sun, Transverse asymptotic  stability of  line solitary waves for the ionic Euler Poisson system, arxiv

F. Rousset, P. Su, Well-posedness of the motion of a rigid body immersed in a compressible inviscid fluid, arxiv

B. Guelmame, T. Hmidi, H. Houamed, F. Rousset, Singular traveling waves for the Euler Poisson system, arxiv

K.Marsden, F. Rousset, K. Schratz, A splitting scheme for the wave maps at low regularity, arxiv

Publications 

D. Han-Kwan, T. T. Nguyen, F. Rousset, Linear Landau damping for the Vlasov-Maxwell system in R3, Ann. PDE 11 (2025), Paper No. 26. arxiv

F. Rousset, K. Schratz, Resonances as a computational tool, Found. Comput. Math. 25 (2025), 1879–1906.arxiv

L. Ji, A. Ostermann, F. Rousset, K. Schratz, Low regularity error estimates for the time integration of 2D NLS, IMA J. Numer. Anal. 45 (2025), 2023–2059.arxiv

F. Rousset, C. Sun, Transverse linear stability of one-dimensional solitary gravity water waves, Arch. Ration. Mech. Anal. 249 (2025), Paper No. 36.arxiv

L. Ji, A. Ostermann, F. Rousset, K. Schratz, Low regularity full error estimates for the cubic nonlinear Schrödinger equation, SIAM J. Numer. Anal. 62 (2024), 2071–2086.arxiv

A. Ostermann, F. Rousset, K. Schratz, Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces, J. Eur. Math. Soc. 25 (2023), 3913–3952.arxiv

N. Masmoudi, F. Rousset, C. Sun, Incompressible limit for the free surface Navier-Stokes system, Ann. PDE 9 (2023), Paper No. 9.arxiv

M. Cabrera Calvo, F. Rousset, K. Schratz, Time integrators for dispersive equations in the long wave regime, Math. Comp. 91 (2022), 2197–2214.arxiv

F. Rousset, K. Schratz, Convergence error estimates at low regularity for time discretizations of KdV, Pure Appl. Anal. 4 (2022), 127–152.arxiv

N. Masmoudi, F. Rousset, C. Sun, Uniform regularity for the compressible Navier-Stokes system with low Mach number in domains with boundaries, J. Math. Pures Appl. (9) 161 (2022), 166–215.arxiv

A. Ostermann, F. Rousset, K. Schratz, Error estimates at low regularity of splitting schemes for NLS, Math. Comp. 91 (2021), 169–182.arxiv

D. Han-Kwan, T. T. Nguyen, F. Rousset, On the linearized Vlasov-Poisson system on the whole space around stable homogeneous equilibria, Comm. Math. Phys. 387 (2021), 1405–1440.arxiv

D. Han-Kwan, T. T. Nguyen, F. Rousset, Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates, Ann. PDE 7 (2021), Paper No. 18.arxiv

E. Faou, R. Horsin, F. Rousset, On linear damping around inhomogeneous stationary states of the Vlasov-HMF model, J. Dynam. Differential Equations 33 (2021), 1531–1577.arxiv

F. Rousset, K. Schratz, A general framework of low regularity integrators, SIAM J. Numer. Anal. 59 (2021), 1735–1768.arxiv

A. Ostermann, F. Rousset, K. Schratz, Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity, Found. Comput. Math. 21 (2021), 725–765.arxiv

F. Rousset, C. Sun, Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system, Ann. Inst. H. Poincaré C Anal. Non Linéaire 38 (2021), 1255–1294.arxiv

C. Courtès, F. Lagoutière, F. Rousset, Error estimates of finite difference schemes for the Korteweg–de Vries equation, IMA J. Numer. Anal. 40 (2020), 628–685.arxiv

E. Grenier, T. T. Nguyen, F. Rousset, A. Soffer, Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method, J. Funct. Anal. 278 (2020), 108339.arxiv

P. Germain, F. Rousset, Long wave limit for Schrödinger maps, J. Eur. Math. Soc. 21 (2019), 2517–2602.arxiv

Gérard-Varet, D. Lacave, T. T. Nguyen, F. Rousset, The vanishing viscosity limit for 2D Navier-Stokes in a rough domain. J. Math. Pures Appl. (9) 119 (2018), 45–84.arxiv

D. Han-Kwan, T. T. Nguyen, F. Rousset, Long time estimates for the Vlasov-Maxwell system in the non-relativistic limit. Comm. Math. Phys. 363 (2018), no. 2, 389–434.arxiv

P. Germain, F. Pusateri, F. Rousset, The nonlinear Schrödinger equation with a potential. Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018), no. 6, 1477–1530.arxiv

E. Faou, R. Horsin, F. Rousset, On numerical Landau damping for splitting methods applied to the Vlasov-HMF model. Found. Comput. Math. 18 (2018), no. 1, 97–134.arxiv

N. Masmoudi, F. Rousset, Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations. Arch. Ration. Mech. Anal. 223 (2017), no. 1, 301–417.arxiv

D. Han-Kwan, F. Rousset, Quasineutral limit for Vlasov-Poisson with Penrose stable data. Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), no. 6, 1445–1495.arxiv

P. Germain, F. Pusateri, F. Rousset, Asymptotic stability of solitons for mKdV. Adv. Math. 299 (2016), 272–330.arxiv

E. Faou, F. Rousset, Landau damping in Sobolev spaces for the Vlasov-HMF model. Arch. Ration. Mech. Anal. 219 (2016), no. 2, 887–902.arxiv

T. M. Elgindi, F. Rousset, Global regularity for some Oldroyd-B type models. Comm. Pure Appl. Math. 68 (2015), no. 11, 2005–2021.arxiv

M. Ming, F. Rousset, N. Tzvetkov, Multi-solitons and related solutions for the water-waves system. SIAM J. Math. Anal. 47 (2015), no. 1, 897–954.arxiv

D. Gérard-Varet, D. Han-Kwan, F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II. J. Éc. polytech. Math. 1 (2014), 343–386.arxiv

D. Gérard-Varet, D. Han-Kwan, F. Rousset, Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries. Indiana Univ. Math. J. 62 (2013), no. 2, 359–402.arxiv

L. G. Farah, F. Rousset, N. Tzvetkov, Oscillatory integral estimates and global well-posedness for the 2D Boussinesq equation. Bull. Braz. Math. Soc. (N.S.) 43 (2012), no. 4, 655–679.

F. Rousset, N. Tzvetkov, Stability and instability of the KdV solitary wave under the KP-I flow. Comm. Math. Phys. 313 (2012), no. 1, 155–173.arxiv

N. Masmoudi, F. Rousset, Uniform regularity for the Navier-Stokes equation with Navier boundary condition. Arch. Ration. Mech. Anal. 203 (2012), no. 2, 529–575.arxiv

F. Rousset, N. Tzvetkov, Transverse instability of the line solitary water-waves. Invent. Math. 184 (2011), no. 2, 257–388.arxiv

T. Hmidi, S. Keraani, F. Rousset, Global well-posedness for Euler-Boussinesq system with critical dissipation. Comm. Partial Differential Equations 36 (2011), no. 3, 420–445.arxiv

T. Hmidi, F. Rousset, Global well-posedness for the Euler-Boussinesq system with axisymmetric data. J. Funct. Anal. 260 (2011), no. 3, 745–796.arxiv

T. Hmidi, S. Keraani, F. Rousset, Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation. J. Differential Equations 249 (2010), no. 9, 2147–2174.

T. Hmidi, F. Rousset, Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data. Ann. Inst. H. Poincaré C Anal. Non Linéaire 27 (2010), no. 5, 1227–1246.arxiv

F. Rousset, N. Tzvetkov, On the transverse instability of one dimensional capillary-gravity waves. Discrete Contin. Dyn. Syst. Ser. B 13 (2010), no. 4, 859–872.

D. Chiron, F. Rousset, The KdV/KP-I limit of the nonlinear Schrödinger equation. SIAM J. Math. Anal. 42 (2010), no. 1, 64–96.

F. Rousset, N. Tzvetkov, A simple criterion of transverse linear instability for solitary waves. Math. Res. Lett. 17 (2010), no. 1, 157–169.arxiv

E. Caglioti, M. Pulvirenti, F. Rousset, On a constrained 2-D Navier-Stokes equation. Comm. Math. Phys. 290 (2009), no. 2, 651–677.arxiv

F. Rousset, N. Tzvetkov, Transverse nonlinear instability for two-dimensional dispersive models. Ann. Inst. H. Poincaré C Anal. Non Linéaire 26 (2009), no. 2, 477–496.arxiv

D. Chiron, F. Rousset, Geometric optics and boundary layers for nonlinear-Schrödinger equations. Comm. Math. Phys. 288 (2009), no. 2, 503–546.arxiv

N. Masmoudi, F. Rousset, Stability of oscillating boundary layers in rotating fluids. Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), no. 6, 955–1002.

F. Rousset, N. Tzvetkov, Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's. J. Math. Pures Appl. (9) 90 (2008), no. 6, 550–590.arxiv

E. Caglioti, M. Pulvirenti, F. Rousset, The 2D constrained Navier-Stokes equation and intermediate asymptotics. J. Phys. A 41 (2008), no. 34, 344001.arxiv

E. Caglioti, F. Rousset, Long time estimates in the mean field limit. Arch. Ration. Mech. Anal. 190 (2008), no. 3, 517–547.

F. Gallaire, F. Rousset, Spectral stability implies nonlinear stability for incompressible boundary layers. Indiana Univ. Math. J. 57 (2008), no. 4, 1959–1975.

E. Caglioti, F. Rousset, Quasi-stationary states for particle systems in the mean-field limit. J. Stat. Phys. 129 (2007), no. 2, 241–263.

F. Gallaire, D. Gérard-Varet, F. Rousset, Three-dimensional instability of planar flows. Arch. Ration. Mech. Anal. 186 (2007), no. 3, 423–475.

D. Gérard-Varet, F. Rousset, Shear layer solutions of incompressible MHD and dynamo effect. Ann. Inst. H. Poincaré C Anal. Non Linéaire 24 (2007), no. 5, 677–710.

E. Caglioti, F. Rousset, Long time behavior of particle systems in the mean field limit. Commun. Math. Sci. 5 (2007), suppl. 1, 11–19.

F. Rousset, Asymptotic behavior of geophysical fluids in highly rotating balls. Z. Angew. Math. Phys. 58 (2007), no. 1, 53–67.

R. Natalini, F. Rousset, Convergence of a singular Euler-Poisson approximation of the incompressible Navier-Stokes equations. Proc. Amer. Math. Soc. 134 (2006), no. 8, 2251–2258.

F. Rousset, Stability of large amplitude Ekman-Hartmann boundary layers in MHD: the case of ill-prepared data. Comm. Math. Phys. 259 (2005), no. 1, 223–256.

E. Grenier, C. K. R. T. Jones, F. Rousset, B. Sandstede, Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory. Nonlinearity 18 (2005), no. 2, 465–483.

F. Rousset, Characteristic boundary layers in real vanishing viscosity limits. J. Differential Equations 210 (2005), no. 1, 25–64.

F. Rousset, Stability of large Ekman boundary layers in rotating fluids. Arch. Ration. Mech. Anal. 172 (2004), no. 2, 213–245.

F. Rousset, Large mixed Ekman-Hartmann boundary layers in magnetohydrodynamics. Nonlinearity 17 (2004), no. 2, 503–518.

S. Benzoni-Gavage, P. Huot, F. Rousset, Nonlinear stability of semidiscrete shock waves. SIAM J. Math. Anal. 35 (2003), no. 3, 639–707.

F. Rousset, Viscous approximation of strong shocks of systems of conservation laws. SIAM J. Math. Anal. 35 (2003), no. 2, 492–519.

F. Rousset, Stability of small amplitude boundary layers for mixed hyperbolic-parabolic systems. Trans. Amer. Math. Soc. 355 (2003), no. 7, 2991–3008.

S. Benzoni-Gavage, F. Rousset, D. Serre, K. Zumbrun, Generic types and transitions in hyperbolic initial-boundary-value problems. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 5, 1073–1104.

F. Rousset, The residual boundary conditions coming from the real vanishing viscosity method. Discrete Contin. Dyn. Syst. 8 (2002), no. 3, 605–625.

E. Grenier, F. Rousset, Stability of one-dimensional boundary layers by using Green's functions. Comm. Pure Appl. Math. 54 (2001), no. 11, 1343–1385.

F. Rousset, Inviscid boundary conditions and stability of viscous boundary layers. Asymptot. Anal. 26 (2001), no. 3-4, 285–306.