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THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

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Acta Mathematica Scientia 2021年第1期41卷 319-336页

作者： hakho hong Institute of Mathematics State Academy of SciencesPyongyangD P R Korea

In this paper,we consider an inflow problem for the non-isentropic Navier-StokesPoisson system in a half line(0,∞).For the general gas including ideal polytropic gas,we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4×4 system of autonomous ordinary differential *** also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.

关键词： Navier-Stokes-Poisson system inflow problem stationary solution existence stability

ZERO DISSIPATION LIMIT TO CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS

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Acta Mathematica Scientia 2016年第1期36卷 157-172页

作者： hakho hong Institute of Mathematics Academy of Sciences

The zero dissipation limit to the contact discontinuities for one-dimensional com- pressible Navier-Stokes equations was recently proved for ideal polytropic gas （see Huang et al. [15, 22] and Ma [31]）, but there is few result for general gases including ideal polytropic gas. We prove that if the solution to the corresponding Euler system of general gas satisfying （1.4） is piecewise constant with a contact discontinuity, then there exist smooth solutions to Navier-Stokes equations which converge to the inviscid solutions at a rate of k1/4 as the heat-conductivity coefficient k tends to zero. The key is to construct a viscous contact wave of general gas suitable to our proof （see Section 2）. Notice that we have no need to restrict the strength of the contact discontinuity to be small.

关键词： zero dissipation limit Navier-Stokes equations contact discontinuity generalgas

Stability of Viscous Contact Wave for Compressible Navier-Stokes Equations with a Large Initial Perturbation

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Acta Mathematicae Applicatae Sinica 2015年第1期31卷 191-212页

作者： hakho hong Institute of Mathematics Academy of Sciences

The viscous contact wave for the compressible Navier-Stokes equations has recently been shown to be asymptotically stable provided that all the L2 norms of initial perturbations, their derivatives and/or anti-derivatives axe small. The main purpose of this paper is to study the asymptotic stability and convergence rate of the viscous contact wave with a large initial perturbation. For this purpose, we introduce a positive number l in the construction of a smooth approximation of the contact discontinuity for the compressible Euler equations and then we make the quantity l to be sufficiently large in order to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. This makes for us to estimate the L2 norms of the solution and its derivative for perturbation system without assuming that L2 norms of the anti-derivatives and the derivatives of initial perturbations are small.

关键词： the compressible Navier-Stokes equations contact discontinuity stability decay rate large initialperturbation

ZERO DISSIPATION LIMIT TO A RIEMANN SOLUTION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS

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Acta Mathematica Scientia 2017年第5期37卷 1177-1208页

作者： hakho hong 王腾 Institute of Mathematics State Academy of SciencesPyongyangD P R Korea Department of Mathematics School of ScienceBeijing Forestry UniversityBeijing 100083China

For the general gas including ideal polytropic gas, we study the zero dissipation limit problem of the full 1-D compressible Navier-Stokes equations toward the superposition of contact discontinuity and two rarefaction waves. In the case of both smooth and Riemann initial data, we show that if the solutions to the corresponding Euler system consist of the composite wave of two rarefaction wave and contact discontinuity, then there exist solutions to Navier-Stokes equations which converge to the Riemman solutions away from the initial layer with a decay rate in any fixed time interval as the viscosity and the heat-conductivity coefficients tend to zero. The proof is based on scaling arguments, the construction of the approximate profiles and delicate energy estimates. Notice that we have no need to restrict the strengths of the contact discontinuity and rarefaction waves to be small.

关键词： zero dissipation limit compressible Navier-Stokes equations contact discontinuity rarefaction wave general gas

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

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Acta Mathematica Scientia 2012年第1期32卷 389-412页

作者： hakho hong Feimin Huang Institute of Mathematics Academy of Sciences Pyonyang DPR of Korea Institute of Applied Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100190 China

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

关键词： compressible Navier-Stokes equations free boundary superposition of shockwave and contact discontinuity stability

THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D

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Acta Mathematica Scientia 2023年第5期43卷 2133-2158页

作者：陈亚洲 hakho hong 施小丁 College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing 100029China Address Institute of Mathematics State Academy of SciencesPyongyangD P R Korea

This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard *** model is usually used to describe the motion of immiscible two-phase flows with a diffusion *** the periodic boundary value problem of this system in torus T3,we prove that there exists a global unique strong solution near the phase separation state,which means that no vacuum,shock wave,mass concentration,interface collision or rupture will be developed in finite ***,we establish the large time behavior of the global strong solution of this *** particular,we find that the phase field decays algebraically to the phase separation state.

关键词： Navier-Stokes/Cahn-Hilliard system strong solution existence uniqueness large-time behavior

Global Existence of Smooth Solutions for the Diffusion Approximation Model of General Gas in Radiation Hydrodynamics

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Acta Mathematica Sinica,English Series 2023年第10期39卷 1855-1873页

作者： Hyejong KIM hakho hong Jongsung KIM Graduate School Kim Hyong Jik University of EducationPyongyangDemocratic People’s Republic of Korea Institute of Mathematics State Academy of SciencesPyongyangDemocratic People’s Republic of Korea School of Mathematics University of Mechanical Engineering PyongyangPyongyangDemocratic People’s Republic of Korea

In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation *** existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic ***,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.

关键词： Radiation hydrodynamics diffusion approximation model existence convergence rate

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen hakho hong Xiao-ding Shi Department of Mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China Institute of Mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate