60 citations · 271 across the 17 of their papers we have counts for
21 papers
Traveling wave solutions to the one-phase Muskat problem: existence and stability
Huy Q. Nguyen, Ian Tice
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitat…
Coercivity of the Dirichlet-to-Neumann operator and applications to the Muskat problem
Huy Q. Nguyen
We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neuman…
Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries
Theodore D. Drivas, Huy Q. Nguyen, Camilla Nobili
We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies wi…
Remarks on the solution map for Yudovich solutions of the Euler equations
Huy Q. Nguyen
Consider Yudovich solutions to the incompressible Euler equations with bounded initial vorticity in bounded planar domains or in . We present a purely Lagrangian proo…
Self-similar solutions for the Muskat equation
Eduardo García-Juárez, Javier Gómez-Serrano, Huy Q. Nguyen +1
We show the existence of self-similar solutions for the Muskat equation. These solutions are parameterized by ; they are exact corners of slope at and become s…
Well-posedness for SQG sharp fronts with unbounded curvature
Francisco Gancedo, Huy Q. Nguyen, Neel Patel
Patch solutions for the surface quasigeostrophic (SQG) equation model sharp temperature fronts in atmospheric and oceanic flows. We establish local well-posedness for SQG sharp fro…
Global solutions for the Muskat problem in the scaling invariant Besov space
Huy Q. Nguyen
The one-phase and two-phase Muskat problems with arbitrary viscosity contrast are studied in all dimensions. They are quasilinear parabolic equations for the graph free boundary. W…
The vanishing surface tension limit of the Muskat problem
Patrick T. Flynn, Huy Q. Nguyen
The Muskat problem, in its general setting, concerns the interface evolution between two incompressible fluids of different densities and viscosities in porous media. The interface…
On well-posedness of the Muskat problem with surface tension
Huy Q. Nguyen
We consider the Muskat problem with surface tension for one fluid or two fluids, with or without viscosity jump, with infinite depth or Lipschitz rigid boundaries, and in arbitrary…
A paradifferential approach for well-posedness of the Muskat problem
Huy Q. Nguyen, Benoît Pausader
We study the Muskat problem for one fluid or two fluids, with or without viscosity jump, with or without rigid boundaries, and in arbitrary space dimension of the interface. Th…
On global stability of optimal rearrangement maps
Huy Q. Nguyen, Toan T. Nguyen
We study the nonlocal vectorial transport equation on bounded domains of where denotes the Leray projecto…
Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
Theodore D. Drivas, Huy Q. Nguyen
We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime weak limit of Leray--Hop…
Inviscid limit for SQG in bounded domains
Peter Constantin, Mihaela Ignatova, Huy Nguyen
We prove that the limit of any weakly convergent sequence of Leray-Hopf solutions of dissipative SQG equations is a weak solution of the inviscid SQG equation in bounded domains.
Onsager's conjecture and anomalous dissipation on domains with boundary
Theodore D. Drivas, Huy Q. Nguyen
We give a localized regularity condition for energy conservation of weak solutions of the Euler equations on a domain , , with boundary. In the bulk…
Compressible fluids and active potentials
Peter Constantin, Theodore D. Drivas, Huy Q. Nguyen +1
We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion…
On singularity formation in a Hele-Shaw model
Peter Constantin, Tarek Elgindi, Huy Nguyen +1
We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in \cite{CDGKSZ93} and widely studied since. The model cons…
Local and global strong solutions for SQG in bounded domains
Peter Constantin, Huy Quang Nguyen
We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of . When fractional Dirichlet Laplacian dissipation is adde…
Global weak solutions for generalized SQG in bounded domains
Huy Quang Nguyen
We prove the existence of global weak solutions for a family of generalized inviscid surface-quasi geostrophic (SQG) equations in bounded domains of the plane. In these equat…
Global weak solutions for SQG in bounded domains
Peter Constantin, Huy Quang Nguyen
We prove existence of global weak solutions of the inviscid SQG equation in bounded domains.
A sharp Cauchy theory for the 2D gravity-capillary waves
Quang-Huy Nguyen
This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. We prove that the Cauchy problem in Sobolev spaces is…
Sharp Strichartz estimates for water waves systems
Quang-Huy Nguyen
Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz est…