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

TEACHING: In the Spring 2015 Semester, I am teaching PDE2. Below are lecture notes and Homework:

**Notes 1.** **HW1.**

**Notes 2.** **HW2.**

**Notes 3.** **HW3.**

**Notes 4.** **HW4.**

**Notes 5.** **HW5.**

**Notes 6.** **HW6.**

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"**.

Since January 2015, I am an Associate Professor at the **Courant Institute.**

I am an editor for **DCDS-A**

Current PhD students

**James Fennell**

**Nicolas Laillet** (jointly with Isabelle Gallagher)

Domingos Lopes

**Klaus Widmayer**

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.

- **On the continuous resonant equation for NLS: I. Deterministic analysis**, with Laurent Thomann and Zaher Hani.

- **On the continuous resonant equation for NLS: II. Statistical analysis**, with Laurent Thomann and Zaher Hani.