Huy Nguyen
Tamarkin Assistant Professor
Brown University
Contact Info
Department of Mathematics
Box 1917
Brown University
151 Thayer Street
Providence, RI 02912
Email: hnguyen@math.brown.edu
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.
Curriculum
Vitae
Research
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.
My current research is partially supported by the NSF grant DMS-1907776.
My preprints are available at my arXiv
page and my Google
Scholar page.
Free-boundary problems in porous media
- Global solutions for the
Muskat problem in the scaling invariant Besov space. arXiv
- (with H. Dong and F.
Gancedo) Global well-posedness for the one-phase Muskat problem. arXiv.
- (with P. Flynn) The
vanishing surface tension limit of the Muskat problem. Communication
in Mathematical Physics (2021).
arXiv.
- On well-posedness of the
Muskat problem with surface tension.
Advances in Mathematics
(2020). arXiv.
- (with B. Pausader) A
paradifferential approach for well-posedness of the Muskat problem.
Archive
for Rational Mechanics and Analysis (2020). arXiv.
Water
waves
- (with W. A. Strauss) Proof
of modulational instability of Stokes waves in deep water. arXiv,
to appear in Communication
on Pure and Applied Mathematics.
- Sharp Strichartz estimates for water waves systems.
Transactions of the American Mathematical Society (2018). arXiv.
- A
sharp Cauchy theory for 2D gravity-capillary water waves. Annales
de l'Institut Henri Poincare (C) Analyse Non Lineaire
(2017). arXiv.
- (with T. de Poyferre) Strichartz
estimates and local existence for the gravity-capillary water
waves with non-Lipschitz initial velocity. Journal
of Differential Equations (2016). arXiv.
- (with T. de Poyferre) A
paradifferential reduction for the gravity-capillary waves
system at low regularity and applications. Bulletin
de la Societe Mathematique de France (2017). arXiv.
- A
pseudo-local property of gravity water waves system. SIAM
Journal of Mathematical Analysis (2016). arXiv.
- Hadamard
well-posedness of the gravity water waves system. Journal
of Hyperbolic Differential Equations (2016). arXiv.
Active
scalars and active vectors in bounded domains
- (with F. Gancedo and N. Patel)
Well-posedness for SQG sharp fronts with unbounded curvature. arXiv.
- (with Toan T. Nguyen) On
global stability of optimal rearrangement maps. Archive for Rational
Mechanics and Analysis (2020). arXiv.
- (with
P. Constantin, M. Ignatova) Inviscid limit for SQG in bounded
domains. SIAM Journal of Mathematical
Analysis
(2018).
arXiv.
- (with P. Constantin)
Local and global strong solutions for SQG in bounded domains.
Physica D-Special Issue
dedicated to Edriss Titi (2018).
arXiv.
- Global
weak solutions for generalized SQG in bounded domains.
Analysis
&
PDE (2018). arXiv.
- (with P. Constantin)
Global
weak solutions for SQG in bounded domains.
Communication on Pure and Applied Mathematics (2018). arXiv.
Fundamental equations and lubrication models in fluid mechanics
- (with P. Constantin, T. D.
Drivas, Federico Pasqualotto) Compressible
fluids and active potentials, Annales
de l'Institut Henri Poincare (C) Analyse Non Lineaire
(2020). arXiv.
- (with P. Constantin, T. Elgindi,
V. Vicol) On
singularity formation in a Hele-Shaw model, Communication
in Mathematical Physics (2018). arXiv.
- (with T. D. Drivas) Remarks
on the emergence of weak Euler solutions in the vanishing viscosity
limit. Journal of Nonlinear
Science (2019). arXiv.
- (with T. D. Drivas)
Onsager's conjecture and
anomalous dissipation on domains with boundary. SIAM
Journal of
Mathematical Analysis
(2018). arXiv.
Collaborators:
P. Constantin (Princeton U), T. de Poyferre (UC Berkeley), H. Dong
(Brown U), T. D. Drivas (Princeton U), T. Elgindi (Duke U), P.
Flynn (Brown U), F. Gancedo (Sevilla), M. Ignatova (Temple
U), Toan
Nguyen (Penn State), N. Patel (U. Michigan), F.
Pasqualotto (UC Berkeley), N. Patel (U. Michigan), B. Pausader (Brown
U), W.
Strauss (Brown U), V. Vicol (Courant).
Teaching at Brown
- Summer 2021: Math 0180-Intermediate Calculus, and Math 1010:
Analysis, functions of one variable.
- Spring 2021: Graduate PDE
- Fall 2020: no teaching
- Spring 2020: Math 0180-Intermediate Calculus (2 sections).
- Fall 2019: Math 1110-Ordinary Differential Equations.
- Spring 2019: Math 0180-Intermediate Calculus.
- Fall 2018: Math 0100-Introductory Calculus II, and Math
1110-Ordinary Differential Equations.