O love, could thou and I with fate conspire To grasp this sorry scheme of things entire, Might we not smash it to bits And mould it closer to our hearts' desire? -- Omar Khayyam, tr. Fitz Gerald

Dispersive Equations

19. Scattering for the two dimensional NLS with exponential nonlinearity, with M. Majdoub, N. Masmoudi and K. Nakanishi: (To appear in Nonlinearity [pdf])

18. Threshold solutions in the case of Mass-shift for the critical nonlinear Klein-Gordon equation , with N. Masmoudi and K. Nakanishi: (To appear in Transactions of the AMS [pdf])

17. Blow-up solutions of quasilinear hyperbolic equation with critical Sobolev exponent", with A. Lyaghfouri.Mathematical Modelling of Natural Phenomena, V. 7, issue 02, pp. 66-76, 2012. 16. Existence of a ground state and blow-up for a nonlinear Schroedinger equation with critical growth, with T. Akahori, H. Kikuchi and H. Nawa (To appear in Diff. and Integral Equa. Preprint [pdf])

15. Strichartz type estimates and the wellposedness of an energy critical 2D wave equation in a bounded domain , with R. Jrad (Journal of Diff. Equa., Vol 250, N 9, 3740-3771, 2011. Preprint available in ArXiv).

14. Well and Ill-posedness issues for energy supercritical. (To appear in Analysis \& PDE. Preprint available in: ArXiv)

13. Scattering threshold for the focusing nonlinear Klein-Gordon equation, with N. Masmoudi and K. Nakanishi. (To appear in Analysis & PDE. Preprint available in: ArXiv)

12. Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary Growth with L. Aloui and K. Nakanishi. (. Preprint available in ArXiv). Preprint available in: ArXiv ).

11. Scattering for the two dimensional energy-critical nonlinear wave equations, with M. Majdoub, N. Masmoudi and K. Nakanishi. Duke Math. Journal, Vol. 152, N 2, 287-329. Preprint available in: ArXiv

10. Instability of super-critical waves: Theory and computation , with P. Guyenne, Journal Mathematics and Computers in Simulation on Nonlinear Waves: Computation and Theory 80 (2009) 2-9. Preprint [pdf] .

9. Energy critical NLS in two space dimensions, with J. Colliander, M. Majdoub and N. Masmoudi. Journal of Hyperbolic Diff. Equa. V. 6, Issue: 3(2009) pp. 549-575. Preprint available in: ArXiv.

8. Ill-posedness of $H^1$-supercritical waves, with M. Majdoub and N. Masmoudi. C. R. Math. Acad. Sci. Paris 345 (2007), no. 3, 133--138. Preprint [pdf]

7. On the Local Solvability for a Quasilinear Cubic Wave Equation , with J. Azzouz, Hokkaido Math. J. 36 (2007), no. 2, 383--416. Preprint [pdf]

6. Global Wellposedness for a 2D Semi-Linear Klein-Gordon Equation, with M. Majdoub and N. Masmoudi, Communications on Pure and Applied Math 59 (2006), no. 11, 1639--1658 (Access required). Preprint [pdf]

5. A Double Logarithmic Inequality with a Sharp Constant, with M. Majdoub and N. Masmoudi, Proc. Amer. Math. Soc. 135 (2007), no. 1, 87--97. Preprint [pdf]

4. Geometric-Optics for Nonlinear Concentrating Waves in Focusing and Non-Focusing Two Geometries, Commun. Contemp. Math. 6 (2004), No 1, 1-23(Access required). Preprint [pdf]

3. Comparaison Des Ondes Lin\'eaires et Non-lin\'eaires \`a Coefficients Variables, with M. Majdoub, Bull. Soc. Math. Belgique 10 (2003) No 2, 299-312 (Access required). Preprint [pdf]

2. Existence, en Grand Temps, de Solutions pour l'\'Equation des Ondes Semi-Lin\'eaire Critique \`a Coefficients Variables, with M. Majdoub, Bull. Soc. Math. France 131 (2003) No 1, 1-22 (Access required). Preprint [pdf]

1. Existence Globale de Solutions pour l'\'Equation des Ondes Semi-Lin\'eaire Critique \`a Coefficients Variables, with M. Majdoub, Comptes- Rendus de l'Acad\'emie des Sciences de Paris (1999), S\'erie I Vol. No 328, 579-584 (Access required). Preprint [pdf]

Fluid Mechanics

6. A contraction argument for two-dimensional spiking neuron model, with E. Foxall, R. Edwards and P. Van Den Drissche (To appear in SIAM J. Applied Dyna.Systems. Preprint available [pdf], and in ArXiv))

5. Global small solutions for the Navier-Stokes-Maxwell system, with S. Keraani (SIAM J. Math. Anal. vol 43, N 5, pp. 2275-2295. Preprint available in ArXiv).

4. Construction of suitable weak solutions of the Navier-Stokes equations, with A. Biryuk and W. Craig, Stochastic analysis and partial differential equations, 1--18, Contemp. Math., 429, Amer. Math. Soc., Providence, RI, 2007. Preprint [pdf]

3. Asymptotic Study of a Magneto-Hydro-Dynamic System, with J. B. Ameur and M. Majdoub, Differential and Integral Equations, 18 (2005), no. 3, 299--324 (Access required). Preprint [pdf]

2. Existence et Unicit\'e pour le Syst\`eme de Navier-Stokes Axisym\'etrique, with I. Gallagher and M. Majdoub, Comm. Partial Differential Equations (2002), 26, No 5-6, 883-907 (Access required). Preprint [pdf]

1. Solutions Axisym\'etriques des \'Equations de Navier-Stokes, with I. Gallagher and M. Majdoub, Comptes- Rendus de l'Acad\'emie des Sciences de Paris (2000), S\'erie I Vol. No 330,, 791-794 (Access required). Preprint [pdf]

Submitted papers & Preprints

  • Well posedness and unconditional non uniqueness for a 2D semilinear heat equation , with R. Jrad, M. Majdoub and T. Saanouni (submitted. Preprint available in ArXiv).

  • T. Akahori, S. Ibrahim, H. Kikuchi and H. Nawa: Existence of a ground state and scattering for a nonlinear Schroedinger equation with critical growth. (Submitted to Selecta Mathematicas. Preprint available at ArXiv).)

  • Long-time solvability of the Navier-Stokes-Boussinesq equations with almost periodic large initial data, with T. Yoneda (submitted. Preprint [pdf], and Preprint available in ArXiv)

  • E. Foxal, S. Ibrahim and T. Yoneda: Streamline concentration and application to the incompressible Navier-Stokes equations, with E. Foxal and T. Yoneda (submitted. Preprint [pdf], and Preprint available in ArXiv)

  • Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data, with T. Yoneda (submitted. Preprint [pdf], and Preprint available in ArXiv)

  • Trudinger-Moser inequality on the whole plane with the exact growth condition, with N. Masmoudi and K. Nakanishi: (submitted. Preprint [pdf])

  • Remarks on the Uniqueness of Weak solutions to the Navier-Stokes System, with A. Biryuk and W. Craig. (In progress)

  • Ill-posedness of supercritical NLS and NLW equations, with N. Burq and P. Gerard. Not published paper [pdf]

    Conference proceedings & Recent Talks

  • Steklov Mathematical Institute, Moscow-Russia, International Workshop on Mathematical Hydrodynamics, June12-17, 2006.

  • University of Calgary, New results in two space dimensions for energy-critical NLS and NLW equations, 2006. [pdf]

  • Mathematisches Forschungsinstitut Oberwolfach, Nonlinear Waves and Dispersive Equations. Reports No. 50/2004

  • First French-Tunisian meeting on PDE. Proceeding editors, B. Dehman, G. Lebeau, C. Zuily. Preprint [pdf]