Pierre Germain

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







I am teaching Functional Analysis this semester.
Homework for Sep 11: exercises 1.2, 1.4, 1.5, 1.6, 1.9 (in Brezis' textbook)
Homework for Sep 18: exercises 1.14, 1.17, 1.20, 1.23, 1.26
Homework for Sep 25: exercises 2.1, 2.5, 2.6, 2.9
Homework for Oct 2: exercises 3.1, 3.2, 3.3, 3.6, 3.8
Homework for Oct 16 (no class on Oct 9!): exercises 3.18, 3.32, problem 13 (at the end of the textbook)
Homework for Nov 13: exercises 6.1, 6.4, 6.11, 6.18, 6.19
Homework for Nov 20: exercises 6.23, 6.26
Homework for Dec 4: exercises 8.22, 8.26, 8.30
Homework for Dec 11: problem 46





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

Here is my CV.

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

Since January 2017, I am a Professor at the Courant Institute.

I am an editor for Communications on Pure and Applied Mathematics, the Graduate Journal of Mathematics, the Journal of Hyperbolic Differential Equations and DCDS-A

Former PhD students
Nicolas Laillet (jointly with Isabelle Gallagher)
Domingos Lopes
Klaus Widmayer
James Fennell

Current PhD students
Tristan Leger
Gavin Stewart





A few talks available in video

Big box limit for 2D NLS, Bonn, July 2014

Long wave limit for Schrodinger maps, MSRI, October 2015

Stability of the Couette flow, IHES, June 2016

Uniqueness for the supercritical Harmonic Map Heat Flow, Institut Henri Poincare, June 2016





List of publications (most of which can be found on my arxiv frontpage):


Proceedings and survey articles

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

2) From dispersion management to continuous resonant equations, Proceedings of the ICMP 2015.

3) Stability of the Couette flow at high Reynolds number in 2D and 3D, with Jacob Bedrossian and Nader Masmoudi.


Refereed articles

1) 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.

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

3) 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.

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

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

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

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

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

9) 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.

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

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

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

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

14) 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.

15) 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.

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

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

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

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

20) Global existence for the Euler-Maxwell system, with Nader Masmoudi, Ann. Sci. Ec. Norm. Super. (4) 47 (2014), no. 3, 469–503.

21) 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.

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

23) 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.

24) Well-posedness of the Navier-Stokes-Maxwell equations, with Slim Ibrahim and Nader Masmoudi, Proc. Roy. Soc. Edinburgh Sect. A 144 (2014), no. 1, 71–86.

25) Global existence for capillary water-waves, with Nader Masmoudi and Jalal Shatah, Comm. Pure Appl. Math. 68 (2015), no. 4, 625–687.

26) The finite energy method for compressible fluids. The Navier-Stokes-Korteweg model, with Philippe LeFloch, Comm. Pure Appl. Math. 69 (2016), no. 1, 3–61.

27) Instability of some equatorially trapped waves, with Adrian Constantin.

28) Nonlinear resonances with a potential: multilinear estimates and an application to NLS, with Zaher Hani and Sam Walsh, Int. Math. Res. Not. IMRN 2015, no. 18, 8484–8544.

29) The weakly nonlinear large box limit of the 2D cubic nonlinear Schrodinger equation, with Erwan Faou and Zaher Hani, J. Amer. Math. Soc. 29 (2016), no. 4, 915–982.

30) Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3, with Frederic Bernicot, Arch. Ration. Mech. Anal. 214 (2014), no. 2, 617–669.

31) An extension of the Derrida-Lebowitz-Speer-Spohn equation, with Charles Bordenave, J. Phys. A 48 (2015), no. 48, 485205

32) On the continuous resonant equation for NLS: I. Deterministic analysis, with Laurent Thomann and Zaher Hani, J. Math. Pures Appl. (9) 105 (2016), no. 1, 131–163.

33) On the continuous resonant equation for NLS: II. Statistical study, with Laurent Thomann and Zaher Hani, Anal. PDE 8 (2015), no. 7, 1733–1756.

34) Asymptotic stability of solitons for mKdV, with Fabio Pusateri and Frederic Rousset, Adv. Math. 299 (2016), 272–330.

35) Dynamics near the subcritical transition of the 3D Couette flow I: Below threshold case, with Jacob Bedrossian and Nader Masmoudi.

36) Dynamics near the subcritical transition of the 3D Couette flow II: Above threshold case, with Jacob Bedrossian and Nader Masmoudi.

37) On the stability threshold for the 3D Couette flow in Sobolev regularity, with Jacob Bedrossian and Nader Masmoudi, Ann. of Math. (2) 185 (2017), no. 2, 541–608.

38) On the high frequency limit of the LLL equation, with Laurent Thomann, Quart. Appl. Math. 74 (2016), no. 4, 633–641.

39) On uniqueness for the Harmonic Map Heat Flow in supercritical dimension, with Tej-Eddine Ghoul and Hideyuki Miura. Comm. Pure Appl. Math. 70 (2017), no. 12, 2247–2299.

40) Long wave limit for Schrodinger maps, with Frederic Rousset.

41) Effective dynamics of the nonlinear Schrodinger equation on large domains, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah, Comm. Pure Appl. Math. 71 (2018), no. 7, 1407–1460.

42) Analysis of the (CR) equation in higher dimensions, with Tristan Buckmaster, Zaher Hani, and Jalal Shatah.

43) Strichartz estimates for the Schrodinger equation on irrational tori, with Yu Deng and Larry Guth, J. Funct. Anal. 273 (2017), no. 9, 2846-2869.

44) Growth of solutions of NLS on irrational tori, with Yu Deng.

45) The nonlinear Schrodinger equation with a potential in dimension 1, with Fabio Pusateri and Frederic Rousset, Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 6, 1477–1530.

46) On the Cubic Lowest Landau Level Equation, with Patrick Gerard and Laurent Thomann.

47) Compactons and their variational properties for degenerate KdV and NLS in dimension 1, with Benjamin Harrop-Griffiths and Jeremy Marzuola.

48) Existence and uniqueness of solutions for a quasilinear KdV equation with degenerate dispersion, with Benjamin Harrop-Griffiths and Jeremy Marzuola.

49) Optimal local well-posedness theory for the kinetic wave equation, with Alexandru Ionescu and Minh-Binh Tran.

50) Vortex filament solutions of the Navier-Stokes equations, with Jacob Bedrossian and Benjamin Harrop-Griffiths.