Huy NguyenTamarkin Assistant Professor
Contact InfoDepartment of Mathematics
151 Thayer Street
Providence, RI 02912
I am a Tamarkin Asisstant Professor in the mathematics department at Brown University.
I completed my PhD in July 2016 at University Paris-Sud XI, Orsay under the supervision of Nicolas Burq. From 2016-2018 I was a Postdoctoral Research Associate and Lecturer in the mathematics department and in PACM at Princeton University where my mentor was Peter Constantin.
My research area is Analysis of Partial Differential Equations. I am currently interested in problems arising in fluid dynamics such as free-boundary problems (e.g water waves, Muskat, Hele-Shaw), active scalar and active vector equations, lubrication models for the theory of drop formation, and vanishing viscosity limit for Navier-Stokes.
Free-boundary problems in porous media
- H. Q. Nguyen and B.
Pausader. Global strong solutions and the infinite depth
limit for the Muskat problem. In preparation.
- P. Flynn and H. Q. Nguyen. The vanishing surface tension limit of the Muskat problem. arXiv:2001.10473.
- H. Q. Nguyen. On well-posedness of the Muskat problem with surface tension. arXiv:1907.11552, submitted (2019).
- H. Q. Nguyen, B. Pausader.
paradifferential approach for well-posedness of the Muskat problem.
Archive for Rational
Mechanics and Analysis, 237(1) 35-100, 2020.
- H. Q. Nguyen. Sharp Strichartz estimates for water waves systems. Transactions of the American Mathematical Society, 370(12) 8797-8832, 2018.
- H. Q. Nguyen. A sharp Cauchy theory for 2D gravity-capillary water waves. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 34 (2017), no. 7, 1793-1836.
- T. de Poyferre, H. Q. Nguyen. Strichartz estimates and local existence for the gravity-capillary water waves with non-Lipschitz initial velocity. Journal of Differential Equations, 261(1) 396-438, 2016.
- T. de Poyferre, H. Q. Nguyen. A paradifferential reduction for the gravity-capillary waves system at low regularity and applications. Bulletin de la Societe Mathematique de France, 145, fascicule 4(2017), 643-710.
- H. Q. Nguyen. A pseudo-local property of gravity water waves system. SIAM Journal of Mathematical Analysis, 48(3) 1988-2027, 2016.
- H. Q. Nguyen. Hadamard well-posedness of the gravity water waves system. Journal of Hyperbolic Differential Equations, 13(4) 791-820, 2016.
- H. Q. Nguyen, Toan T. Nguyen, On global stability of optimal rearrangement maps, arXiv:1901.02964, to appear in Archive for Rational Mechanics and Analysis.
Constantin, M. Ignatova, H. Q. Nguyen. Inviscid
for SQG in bounded domains. SIAM Journal of Mathematical
50(6), 6196-6207, 2018.
- P. Constantin, H. Q. Nguyen. Local and global strong solutions for SQG in bounded domains. Physica D-Special Issue in Honor of Edriss Titi, Vol. 376-378 (2018), 195-203.
- H. Q. Nguyen. Global weak solutions for generalized SQG in bounded domains. Analysis & PDE, Vol. 11 (2018), No. 4, 1029-1047.
- P. Constantin, H. Q. Nguyen. Global weak solutions for SQG in bounded domains. Communication on Pure and Applied Mathematics, 71 (2018), no. 11, 2323-2333.
Fundamental equations and lubrication models in fluid mechanics
- P. Constantin, T. D. Drivas, H. Q. Nguyen, Federico Pasqualotto. Compressible fluids and active potentials, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, (37)1, 145-180, 2020.
- P. Constantin, T. Elgindi, H. Q. Nguyen, V. Vicol. On singularity formation in a Hele-Shaw model, Communication in Mathematical Physics, 363 (2018), no. 1, 139-171.
- T. D. Drivas, H. Q. Nguyen. Remarks
on the emergence of weak Euler solutions in the vanishing
viscosity limit. Journal of Nonlinear Science, 29
(2019), no. 2, 709-721.
- T. D. Drivas, H. Q. Nguyen, Onsager's conjecture and anomalous dissipation on domains with boundary. SIAM Journal of Mathematical Analysis, 50(5), 4785-4811, 2018.
Collaborators: P. Constantin (Princeton U), T. de Poyferre (UC Berkeley), T. D. Drivas (Princeton U), T. Elgindi (UC San Diego), P. Flynn (Brown U), M. Ignatova (Princeton U), T. Nguyen (Penn State), F. Pasqualotto (Princeton U), B. Pausader (Brown U), W. Strauss (Brown U), V. Vicol (Courant).
Teaching at Brown
- Spring 2020: Math 0180-Intermediate Calculus (2 sections).
- Fall 2019: Math 1110-Ordinary Differential Equations. Office hours: Mon 1:30-3:00pm or by appointment.
- Spring 2019: Math 0180-Intermediate Calculus.
- Fall 2018: Math 0100-Introductory Calculus II, and Math 1110-Ordinary Differential Equations.