Version francaise

Pierre Germain

Courant Institute of Mathematical Sciences
New York University
251 Mercer Street
New York, N.Y. 10012-1185
pgermain@cims.nyu.edu

Research domains : fluid mechanics, nonlinear wave equations, harmonic analysis.




Here is my CV.

I defended in 2005 my PhD, which I had prepared under the supervision of Isabelle Gallagher; I defended in 2008 my "Habilitation a diriger des recherches".

I am since September 2010 an Assistant Professor at the Courant Institute.

In the Spring 2014 Semester, I am teaching a class on the Nonlinear Schrodinger equation for which lecture notes are available thanks to Tarek Elgindi!
If you want to contribute to the improvement of these notes, you are very welcome to take part to this collaborative project.



Publications:

- Equations de Navier-Stokes en deux dimensions : existence et comportement asymptotique de solutions d'energie infinie, Bull. Sci. Math. 130 (2006), no. 2, 123--151.

- Multipliers, Paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations, J. Differential Equations 226 (2006), no. 2, 373--428

- Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO-1 , with Natasa Pavlovic and Gigliola Staffilani, Int. Math. Res. Not. IMRN 2007, no. 21.

- Finite energy scattering for the Lorentz-Maxwell equation, Ann. Henri Poincare 9 (2008), no. 5, 927--943.

- Global infinite energy solutions of the critical semilinear wave equation, Rev. Mat. Iberoam. 24 (2008), no. 2, 463--497.

- Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes equation, J. Anal. Math. 105 (2008), 169--196.

- Besov spaces and self-similar solutions for the wave-map equation., Comm. Partial Differential Equations 33 (2008), no. 7-9, 1571--1596.

- The second iterate for the Navier-Stokes equation, J. Funct. Anal. 255 (2008), no. 9, 2248--2264.

- On the existence of smooth self-similar blow up profiles for the wave map equation, Comm. Pure Appl. Math. 62 (2009), no. 5, 706--728.

- Global solutions for 3D quadratic Schroedinger equations, with Nader Masmoudi and Jalal Shatah, Int. Math. Res. Not. IMRN 2009, no. 3, 414--432.

- Self-similar solutions for the Schroedinger map equation, with Jalal Shatah and Chongchun Zeng, Math. Z. 264 (2010), no. 3, 697--707.

- Weak-strong uniqueness for the isentropic compressible Navier-Stokes system, J. Math. Fluid Mech. 13 (2011), no. 1, 137--146.

- Bilinear oscillatory integrals and boundedness for new bilinear multipliers, with Frederic Bernicot, Adv. Math. 225 (2010), no. 4, 1739--1785.

- Global solutions for the gravity water waves equation in dimension 3 (note announcing the result), with Nader Masmoudi and Jalal Shatah, C. R. Math. Acad. Sci. Paris 347 (2009), no. 15-16, 897--902.

- Global solutions for the gravity water waves equation in dimension 3 (full article), with Nader Masmoudi and Jalal Shatah, Ann. of Math. (2) 175 (2012), no. 2, 691--754.

- Global solutions for 2D quadratic Schroedinger equations, with Nader Masmoudi and Jalal Shatah, J. Math. Pures Appl. (9) 97 (2012), no. 5, 505--543.

- Global solutions for coupled Klein-Gordon equations with different speeds, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 6, 2463--2506.

- Space-time resonances, Exp. No 8, Proceedings of the Journees EDP 2010.

- Self-similar expanders of the harmonic map flow, with Melanie Rupflin, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), no. 5, 743--773.

- Boundedness of bilinear multipliers whose symbols have a narrow support, with Frederic Bernicot, J. Anal. Math. 119 (2013), 166--212.

- Global existence for the Euler-Maxwell system, with Nader Masmoudi.

- On the open sea propagation of water waves generated by a moving bed, with Adrian Constantin, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 370 (2012), no. 1964, 1587--1601.

- Bilinear dispersive estimates via space time resonances. Part I: the one-dimensional case, with Frederic Bernicot, Anal. PDE 6 (2013), no. 3, 687-722.

- Non-neutral global solutions for the electron Euler-Poisson system in 3D, with Nader Masmoudi and Benoit Pausader, SIAM J. Math. Anal. 45 (2013), no. 1, 267--278.

- Well-posedness of the Navier-Stokes-Maxwell equations, with Slim Ibrahim and Nader Masmoudi, accepted by the Proceedings of the Royal Society of Edinburgh Section A.

- Global existence for capillary water-waves, with Nader Masmoudi and Jalal Shatah, accepted by Communications in Pure and Applied Mathematics.

- The finite energy method for compressible fluids. The Navier-Stokes-Korteweg model, with Philippe LeFloch.

- Instability of some equatorially trapped waves, with Adrian Constantin.

- Nonlinear resonances with a potential: multilinear estimates and an application to NLS, with Zaher Hani and Sam Walsh.

- The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation, with Erwan Faou and Zaher Hani.

- Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3 , with Frederic Bernicot.

- An extension of the Derrida-Lebowitz-Speer-Spohn equation, with Charles Bordenave.