Preprints

  • The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme II, with Antoine Benoit, may 2024, link to pdf
  • On some stable boundary closures of finite difference schemes for the transport equation, with Tomas Lundquist, january 2020, link to pdf (this note will not be submitted to publication)
  • The amplitude equation for weakly nonlinear reversible phase boundaries, with Sylvie Benzoni-Gavage, link to pdf (this note will not be submitted to publication)

Publications (thematic classification)

(Free) Boundary value problems for hyperbolic systems

  • A priori estimates for 3D incompressible current-vortex sheets, with Alessandro Morando, Paolo Secchi and Paola Trebeschi, link to pdf, Communications in Mathematical Physics (2012), link to final version
  • The hyperbolic region for hyperbolic boundary value problems, link to pdf, Osaka Journal of Mathematics (2011), link to final version (free online)
  • Uniqueness of 2D compressible vortex sheets, with Paolo Secchi, Communications on Pure and Applied Analysis (2009), link to final version
  • Nonlinear compressible vortex sheets in two space dimensions, with Paolo Secchi, Annales Scientifiques de l'Ecole Normale Supérieure (2008), link to final version (free online)
  • Well-posedness of hyperbolic Initial Boundary Value Problems, link to pdf, Journal de Mathématiques Pures et Appliquées (2005), link to final version
  • Stability of contact discontinuities for the nonisentropic Euler equations, with Alessandro Morando, Annali dell'Universita di Ferrara (2004), link to final version
  • On the transition to instability for compressible vortex sheets, with Paolo Secchi, Proceedings of the Royal Society of Edinburgh Section A (2004), link to final version
  • The stability of compressible vortex sheets in two space dimensions, with Paolo Secchi, link to pdf, Indiana University Mathematics Journal (2004), link to final version
  • Weakly stable multidimensional shocks, Annales de l'Institut Henri Poincaré - Analyse non linéaire (2004), link to final version (free online)
  • Stability of multidimensional undercompressive shock waves, Interfaces and Free Boundaries (2003), link to final version (free online)
  • Weak stability of nonuniformly stable multidimensional shocks, SIAM Journal on Mathematical Analysis (2002), link to final version

Geometric optics and weakly nonlinear analysis for hyperbolic problems with boundary conditions

  • Weakly nonlinear surface waves in magnetohydrodynamics, with Olivier Pierre, link to pdf, Asymptotic Analysis (2021), link to final version (the final published version is a short version of the complete work; some supplementary material with the complete proof of the main Theorem can be found on the journal webpage)
  • Geometric optics for surface waves in nonlinear elasticity, with Mark Williams, link to pdf, Memoirs of the American Mathematical Society (2020), link to final version
  • The Mach stem equation and amplification in strongly nonlinear geometric optics, with Mark Williams, link to pdf, American Journal of Mathematics (2017), link to final version
  • Singular pseudodifferential calculus for wavetrains and pulses, with Olivier Guès and Mark Williams, link to pdf, Bulletin de la Société Mathématique de France (2014), link to final version
  • Amplification of pulses in nonlinear geometric optics, with Mark Williams, link to pdf, Journal of Hyperbolic Differential Equations (2014), link to final version
  • Semilinear geometric optics with boundary amplification, with Olivier Guès and Mark Williams, link to pdf, Analysis and PDE (2014), link to final version
  • Nonlinear geometric optics for reflecting uniformly stable pulses, with Mark Williams, link to pdf, Journal of Differential Equations (2013), link to final version
  • On the amplitude equations for weakly nonlinear surface waves, with Sylvie Benzoni-Gavage, link to pdf, Archive for Rational Mechanics and Analysis (2012), link to final version
  • Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, with Olivier Guès and Mark Williams, link to pdf, Communications in Partial Differential Equations (2011), link to final version
  • Geometric optics expansions with amplification for hyperbolic boundary value problems: linear problems, with Olivier Guès, link to pdf, Annales de l'Institut Fourier (2010), link to final version (free online)

Euler equations for compressible fluids

  • On the Mach stem configuration with shallow angle, with Mark Williams, link to pdf, Indiana University Mathematics Journal (2020), link to final version
  • Boundary conditions for the Euler equations, with Sylvie Benzoni-Gavage and Stéphane Aubert, AIAA Journal (2003), link to final version
  • Note on a paper by Robinet, Gressier, Casalis and Moschetta, with Sylvie Benzoni-Gavage and Denis Serre, Journal of Fluid Mechanics (2002), link to final version

Numerical schemes for hyperbolic problems

Hyperbolic systems with relaxation and related models

  • The strong relaxation limit of the multidimensional Euler equations, with Chunjin Lin, link to pdf, Nonlinear Differential Equations and Applications (2013), link to final version
  • Analysis of large amplitude shock profiles for non-equilibrium radiative hydrodynamics: formation of Zeldovich spikes, with Thierry Goudon, Pauline Lafitte and Chunjin Lin, link to pdf, Shock Waves (2012), link to final version
  • Relaxation approximation of the Euler equations, with Christophe Chalons, link to pdf, Journal of Mathematical Analysis and Applications (2008), link to final version
  • Asymptotic stability of shock profiles in radiative hydrodynamics, with Chunjin Lin and Thierry Goudon, Comptes Rendus de l'Académie des Sciences - Série Mathématiques (2007), link to final version
  • The strong relaxation limit of the multidimensional isothermal Euler equations, with Thierry Goudon, Transactions of the American Mathematical Society (2007), link to final version (free online)
  • Entropy-based moment closure for kinetic equations : Riemann problem and invariant regions, with Thierry Goudon, Journal of Hyperbolic Differential Equations (2006), link to final version
  • Shock profiles for nonequilibrium radiating gases, with Chunjin Lin and Thierry Goudon, link to pdf, Physica D (2006), link to final version
  • Diffusion approximation and entropy based moment closure for kinetic equations, with François Golse and Thierry Goudon, Asymptotic Analysis (2005), link to final version

Analysis of partial differential equations (unclassified)

Proceedings

  • Amplitude equations for weakly nonlinear surface waves in variational problems, with Sylvie Benzoni-Gavage, link to pdf, Shocks, singularities and oscillations in nonlinear optics and fluid mechanics, Rome - Italy (2017), link to final version
  • Ondes de surface faiblement non-linéaires, with Sylvie Benzoni-Gavage and Nikolay Tzvetkov, Séminaire Laurent Schwartz (2011-2012), link to final version (free online, in French)
  • Stability of finite difference schemes for hyperbolic initial boundary value problems, Hyp 2010, Beijing - China (2010)
  • Multi-d shock waves and surface waves, with Sylvie Benzoni-Gavage, Hyp 2008, College Park - USA (2008)
  • Shock profiles in radiative hydrodynamics, with Thierry Goudon, Session États de la recherche, Nice - France (2007), link to final version
  • Nonlinear stability of compressible vortex sheets, with Paolo Secchi, Hyp 2006, Lyon - France (2006)
  • Problèmes mixtes hyperboliques bien-posés, Analyse des équations aux dérivées partielles, Forges les eaux - France (2004), link to final version (free online, in French)
  • Stability of compressible vortex sheets, with Paolo Secchi, Equadiff 2003, Hasselt - Belgium (2003)
  • Weak stability of multidimensional shock waves, Hyp 2002, Pasadena - USA (2002)

Lecture notes