P. Nguyen

activity

20132023

most citedEnergy equalities for compressible Navier-Stokes equations

36 citations · 83 across the 26 of their papers we have counts for

collaborators

29 papers

math.AP2023

Semilinear elliptic equations involving fractional Hardy operators

Huyuan Chen, Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Our aim in this article is to study semilinear elliptic equations involving a fractional Hardy operator, an absorption and a Radon source in a weighted distributional sense. We sho…

math.AP2022★ 1 cited

A large class of nonlocal elliptic equations with singular nonlinearities

Rakesh Arora, Phuoc-Tai Nguyen, Vicentiu D. Radulescu

In this work, we address the questions of existence, uniqueness, and boundary behavior of the positive weak-dual solution of equation $L_{γ}^{s} u = F (u)$ , posed in…

math.AP2022★ 3 cited

Semilinear elliptic equations involving power nonlinearities and hardy potentials with boundary singularities

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $Σ \subset \partial Ω$ be a $C^{2}$ compact submanifold without boundary, of dimension $k$ , $0 \leq k \leq N - 1$ . We…

math.AP2022★ 5 cited

Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Phuoc-Truong Huynh, Phuoc-Tai Nguyen

In this paper, we consider a class of integro-differential operators $L$ posed on a $C^{2}$ bounded domain $Ω \subset R^{N}$ with appropriate homogeneous Dirichlet con…

math.AP2022★ 3 cited

Semilinear elliptic Schrödinger equations with singular potentials and absorption terms

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $Σ \subset Ω$ be a compact, $C^{2}$ submanifold without boundary, of dimension $k$ with $0 \leq k < N - 2$ . Put $L_…

math.AP2022

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N > 2$ ) be a $C^{2}$ bounded domain and $Σ \subset Ω$ be a compact, $C^{2}$ submanifold without boundary, of dimension $k$ with $0 \leq k < N - 2$ . Put $L_μ= Δ+…

math.AP2021

Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

Mousomi Bhakta, Moshe Marcus, Phuoc-Tai Nguyen

We study boundary value problems with measure data in smooth bounded domains $Ω$ , for semilinear equations involving Hardy type potentials. Specifically we consider problems of the…

math.AP2021

Semilinear nonlocal elliptic equations with source term and measure data

Phuoc-Truong Huynh, Phuoc-Tai Nguyen

Recently, several works have been carried out in attempt to develop a theory for linear or sublinear elliptic equations involving a general class of nonlocal operators characterize…

math.CV2020

Polynomial Null Solutions to Bosonic Laplacians, Bosonic Bergman and Hardy Spaces

Chao Ding, Phuoc-Tai Nguyen, John Ryan

A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second order conformally invariant differential operator acting on functions taking values in irred…

math.AP2020

Green kernel and Martin kernel of Schrödinger operators with singular potential and application to the B.V.P. for linear elliptic equations

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $K \subset Ω$ be a compact, $C^{2}$ submanifold in $R^{N}$ without boundary, of dimension $k$ with $0\le…

math-ph2020

Boundary value problems in Euclidean space for Bosonic Laplacians

Chao Ding, Phuoc-Tai Nguyen, John Ryan

A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher order…

math.AP2019★ 1 cited

Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential

D. Mukherjee, P. T. Nam, P. T. Nguyen

We consider the focusing nonlinear Schrödinger equation with the critical inverse square potential. We give the first proof of the uniqueness of the ground state solution. Conseque…

math.AP2019

Semilinear elliptic equations with Hardy potential and gradient nonlinearity

Konstantinos Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $δ$ be the distance to $\partial Ω$ . We study positive solutions of equation (E) $- L_{μ} u + g (∣\nabla u ∣) = 0$ …

math.AP2018★ 36 cited

Energy equalities for compressible Navier-Stokes equations

Quoc-Hung Nguyen, Phuoc-Tai Nguyen, Quoc Bao Tang

The energy equalities of compressible Navier-Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient cond…

math.AP2018

On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures

Mousomi Bhakta, Phuoc-Tai Nguyen

We study positive solutions to the fractional Lane-Emden system \begin{equation*} \tag{S}\label{S} \left\{ \begin{aligned} (-Δ)^s u &= v^p+μ\quad &&\text{in } Ω\\ (-Δ)^s v &= u^q+ν…

math.AP2018

Energy conservation for inhomogeneous incompressible and compressible Euler equations

Quoc-Hung Nguyen, Phuoc-Tai Nguyen, Bao Quoc Tang

Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient c…

math.AP2018★ 23 cited

Onsager's conjecture on the energy conservation for solutions of Euler equations in bounded domains

Quoc-Hung Nguyen, Phuoc-Tai Nguyen

The Onsager's conjecture has two parts: conservation of energy, if the exponent is larger than $1/3$ and the possibility of dissipative Euler solutions, if the exponent is less or…

math.AP2018

Schrödinger equations with singular potentials: linear and nonlinear boundary value problems

Moshe Marcus, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $F \subset \partial Ω$ be a $C^{2}$ submanifold of dimension $0 \leq k \leq N - 2$ . Put $δ_{F} (x) = d i s t (x, F)$ , $V=δ…

math.AP2018★ 1 cited

Boundary value problem with measures for fractional elliptic equations involving source nonlinearities

Mousomi Bhakta, Phuoc-Tai Nguyen

We are concerned with positive solutions of equation (E) $(- Δ)^{s} u = f (u)$ in a domain $Ω \subset R^{N}$ ( $N > 2 s$ ), where $s \in (\frac{1}{2}, 1)$ and $f\in C^α_{loc}(\mathbb{R})…

math.AP2017

On the generalized principal eigenvalue of quasilinear operators

Phuoc-Tai Nguyen, Hoang-Hung Vo

The notions of generalized principal eigenvalue for linear second order elliptic operators in general domains introduced by Berestycki et al. \cite{BNV,BR0,BR3} have become a very…

math.AP2017

Boundary singularities of solutions to semilinear fractional equations

Phuoc-Tai Nguyen, Laurent Veron, Laurent Eron

We prove the existence of a solution of (-- $Δ$ ) s u + f (u) = 0 in a smooth bounded domain $Ω$ with a prescribed boundary value $μ$ in the class of positive Radon measures for a la…

math.AP2016

On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a bounded smooth domain and $δ (x) = dist (x, \partial Ω)$ . In this paper, we provide various necessary and sufficient conditions for…

math.AP2016★ 1 cited

Moderate solutions of semilinear elliptic equations with Hardy potential under minimal restrictions on the potential

Moshe Marcus, Vitaly Moroz

We study semilinear elliptic equations with Hardy potential $(E) - L_{μ} u + u^{q} = 0$ in a bounded smooth domain $Ω \subset R^{N}$ . Here $q > 1$ , $L_{μ} = Δ + \frac{μ}{δ _{Ω}^{2}}$ and $…

math.AP2015

Semilinear elliptic equations with Hardy potential and subcritical source term

Phuoc-Tai Nguyen

Let $Ω$ be a smooth bounded domain in $R^{N}$ and $δ (x) = dist (x, \partial Ω)$ . Assume $μ > 0$ , $ν$ is a nonnegative finite measure on $\partial Ω$ and $g \in C(Ω\times…