Slim Ibrahim

My broad area of research is Applied Mathematics with a focus on the Analysis of Partial Differential Equations. Among others, I am working on Nonlinear Partial Differential Equations arising from Quantum Mechanics, Fluid Dynamics, Geophysical flows and more recently Kinetic Models. Questions related to the existence of solutions, their Asymptotic behaviors, and Blow up Analysis are in the core of my research.

Interests

• Applied Mathematics
• Analysis of Partial Differential Equations
• Mathematical Physics
• Fluid Dynamics
• Wave Propagation

Courses

• Fall 2023:
• Spring 2024: MATH 101: Calculus II  MATH 346: Introduction to Partial Differential Equations 
• Summer 2024: MATH 346: Introduction to Partial Differential Equations 

Selected Publications

• Full list and files can be found at http://arxiv.org/find/math/1/au:+Ibrahim_S/0/1/0/all/0/1
• T. Akahori, S. Ibrahim, H. Kikuchi and H. Nawa: "Global dynamic for a nonlinear Schroedinger equation above a ground state with small frequency". Preprint.
• F. Diacu, S. Ibrahim and J. Sniatycki: "The continuous transition of Hamiltonian vector fields through manifolds of constant curvature". Preprint.
• S. Ibrahim, P. G. Lemarie and N. Masmoudi: "Time-periodic forcing and asymptotic stability of the Navier-Stokes-Maxwell equations". Preprint.
• F. Diacu, S. Ibrahim, C. Lind and S. Shen: "The Vlasov-Poisson system for stellar dynamics in spaces of constant curvature". Accepted in Comm. Math. Phys.
• S. Ibrahim: "Global Dynamics for semilinear Schroedinger equations", Canad. Math. Soc. Notes 47 (6), December 2015. https://cms.math.ca/notes/v47/n6/Notesv47n6.pdf.
• D. Arsenio, S. Ibrahim and N. Masmoudi: "A derivation of the Magnetohydrodynamic system from Navier-Stokes-Maxwell systems" Arch. Ration. Mech. Anal. 216 (2015), no. 3, 767–812.
• H. Bahouri, S. Ibrahim and G. Perelman: Scattering for the critical 2-D NLS with exponential growth, Differential and Integral Equations. Vol. 27, N. 3-4, 233-268, 2014.
• C. Cao, S. Ibrahim, K. Nakanishi and E. Titi: Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric. Comm. Math. Phys. 337 (2015), no. 2, 473–482.
• S. Ibrahim, N. Masmoudi and K. Nakanishi: Trudinger-Moser inequality on the whole plane with the exact growth condition. J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 819–835.
• T. Akahori, S. Ibrahim, H. Kikuchi and H. Nawa: Existence of a ground state and scattering for a nonlinear Schroedinger equation with critical growth. Selecta Mathematica (N.S.) 19, N. 2, 545-609, 2013
• E. Foxall, R. Edwards, S. Ibrahim and P. Van Driessche: A contraction argument for a two-dimensional spiking Neuron model. SIAM J. Appl. Dyn. Syst. 11, n 1, 540-566, 2012.
• S. Ibrahim, M. Majdoub, N. Masmoudi and K. Nakanishi: Scattering for the two dimensional NLS with exponential nonlinearity. Nonlinearity, V. 25, issue 6, 1843-1849, 2012.
• S. Ibrahim and S. Keraani. Small global solutions for the coupled Navier-Stokes-Maxwell system. SIAM J. Math. Anal. Vol. 43, No. 5, pp. 2275-2295, 2011.
• S. Ibrahim, N. Masmoudi and K. Nakanishi. Scattering threshold for the focusing nonlinear Klein-Gordon equation. Analysis and PDE. Vol. 4, No. 3, pp. 405-460, 2011.
• Ibrahim and R. Jrad. Strichartz type estimates and the wellposedness of an energy critical 2D wave equation in a bounded domain. Journal of Diff. Equa., Vol 250, N 9, 3740-3771, 2011.
• S. Ibrahim, M. Majdoub, N. Masmoudi and K. Nakanishi. Scattering for a 2D energy-critical nonlinear wave and Schrödinger equations, Duke Math. Journal, Vol. 152, N 2, 287-329, 2009.