10 citations · 31 across the 18 of their papers we have counts for
16 papers · 1 filter
Linear non-divergence parabolic equations in non-cylindrical space-time sets
Luan Hoang, Akif Ibragimov
We study linear parabolic equations of the second order in non-divergence form in a general set which is non-cylindrical with respect to the spatial and time variables. The restric…
An intrinsic expansion approach to the Galerkin approximations for the Navier-Stokes equations (with an appendix by Chengzhang Fu)
Luan Hoang, Michael S. Jolly
We study the Galerkin approximation of the three-dimensional Navier-Stokes equations. In particular, we examine the convergence of these solutions in a sequence of finite dimension…
On compressible fluid flows of Forchheimer-type in rotating heterogeneous porous media
Emine Celik, Luan Hoang, Thinh Kieu
We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boun…
Linear non-divergence elliptic equations in a bounded, infinitely winding planar domain
Luan Hoang, Akif Ibragimov
We study the second order elliptic equations of non-divergence form in a planar domain with complicated geometry. In this case the domain winds around a fixed circle infinitely man…
Asymptotic expansions with subordinate variables for solutions of the Navier-Stokes equations
Luan Hoang
We study the three-dimensional Navier-Stokes equations in a periodic domain with the force decaying in time. Although the force has a certain coherent decay, as time tends to infin…
Intrinsic expansions in large Grashof numbers for the steady states of the Navier-Stokes equations
Luan Hoang, Michael S. Jolly
We enable a theory of intrinsic asymptotic expansions for the steady state solutions of the full Navier-Stokes equations. Such a theory was first developed in Foias et al (2024 Com…
On Galerkin approximations of the Navier-Stokes equations in the limit of large Grashof numbers
Ciprian Foias, Luan Hoang, Michael S. Jolly
We examine how stationary solutions to Galerkin approximations of the Navier--Stokes equations behave in the limit as the Grashof number tends to . An appropriate scali…
Anisotropic flows of Forchheimer-type in porous media and their steady states
Luan Hoang, Thinh Kieu
We study the anisotropic Forchheimer-typed flows for compressible fluids in porous media. The first half of the paper is devoted to understanding the nonlinear structure of the ani…
On the finite time blow-ups for solutions of nonlinear differential equations
Luan Hoang
We study systems of nonlinear ordinary differential equations where the dominant term, with respect to large spatial variables, causes blow-ups and is positively homogeneous of a d…
Slightly Compressible Forchheimer Flows in Rotating Porous Media
Emine Celik, Luan Hoang, Thinh Kieu
We formulate the the generalized Forchheimer equations for the three-dimensional fluid flows in rotating porous media. By implicitly solving the momentum in terms of the pressure's…
Asymptotic expansions in a general system of decaying functions for solutions of the Navier-Stokes equations
Dat Cao, Luan Hoang
We study the long-time dynamics of the Navier-Stokes equations in the three-dimensional periodic domains with a body force decaying in time. We introduce appropriate systems of dec…
Navier and Stokes meet Poincar\' e and Dulac
Ciprian Foias, Luan Hoang, Jean-Claude Saut
This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that that…
Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media
Emine Celik, Luan Hoang, Thinh Kieu
This paper is focused on the generalized Forchheimer flows of compressible fluids in porous media. The gravity effect and other general nonlinear forms of the source terms and boun…
Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations
Luan T. Hoang, Vincent R. Martinez
In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential b…
Maximum estimates for generalized Forchheimer flows in heterogeneous porous media
Emine Celik, Luan Hoang
This article continues our previous study of generalized Forchheimer flows in heterogeneous porous media. Such flows are used to account for deviations from Darcy's law. In heterog…
Generalized Forchheimer flows in heterogeneous porous media
Emine Celik, Luan Hoang
We study the generalized Forchheimer flows of slightly compressible fluids in heterogeneous porous media. The media's porosity and coefficients of the Forchheimer equation are func…