arXiv subjects

Qiangchang Ju

Publications and source records attributed to Qiangchang Ju.

15 recordsLinked to original sources

arXiv2025

Global existence for full compressible Navier-Stokes equations around the Couette flow with a temperature gradient in an infinite channel

This paper is concerned with the two-dimensional full compressible Navier-Stokes equations between two infinite parallel isothermal walls, where the upper wall is moving with a horizontal velocity, while the lower wall is stationary, and there allows a temperature difference between the two walls. It is shown that if the initial state is close to the Couette flow with a temperature gradient, then the global strong solutions exist, provided that the Reynolds and Mach numbers are low and the temperature difference between the two walls is small. The low Mach number limit of the global strong solutions is also shown for the case that both walls maintain the same temperature.

math.AP↗

arXiv2024

Uniform Anisotropic Regularity and Low Mach Number Limit of Non-isentropic Ideal MHD Equations with a Perfectly Conducting Boundary

We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing a special structure contributed by Lorentz force in vorticity analysis, we establish uniform estimates in suitable anisotropic Sobolev spaces with weights of Mach number determined by the number of material derivatives. We also observe that the entropy has the enhanced regularity in the direction of the magnetic field. These two observations help us get rid of the loss of derivatives and weights of Mach number in vorticity analysis caused by the simultaneous appearance of entropy, general initial data and the magnetic field, which is one of the major difficulties that do not appear in Euler equations or the isentropic problems. By utilizing the technique of Alinhac good unknowns, the anti-symmetric structure is preserved in the tangential estimates for the system differenetiated by high-order material derivatives.

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arXiv2023

Non-equilibrium-diffusion limit of the compressible Euler radiation model

We justify rigorously the non-equilibrium-diffusion limit of the compressible Euler model coupled with a radiative transfer equation arising in radiation hydrodynamics. For general initial data, we establish the uniform existence of the solution to the coupled model in $\mathbb{T}^{3}$ and prove the convergence of the solutions to the limiting system in the nonequilibrium-diffusion regime. Moreover, the initial layer for the radiative density is constructed to get the strong convergence in $L^\infty$ norm.

math.AP↗

arXiv2023

Global existence and low mach number limit of strong solutions to the full compressible Navier-Stokes equations around the plane Couette flow

In this paper, we study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the plane Couette flow in a horizontally periodic layer with non-slip and isothermal boundary conditions. It is shown that the plane Couette flow is asymptotically stable for sufficiently small initial perturbations, provided that the Reynolds number, Mach number and temperature difference between the top and the lower walls are small. For the case that both the top and the lower walls maintain the same temperature, we further prove that such global strong solutions converge to a steady solution of the incompressible Navier-Stokes equations as the Mach number goes to zero.

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arXiv2022

Singular Limits for the Navier-Stokes-Poisson Equations of Viscous Plasma with Strong Density Boundary Layer

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric potential. This is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential, which comes from the break-down of the quasi-neutrality near the boundary, and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field.

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arXiv2020

Convergence Rate Estimates for the Low Mach and Alfvén Number Three-Scale Singular Limit of Compressible Ideal Magnetohydrodynamics

Convergence rate estimates are obtained for singular limits of the compressible ideal magnetohydrodynamics equations, in which the Mach and Alfvén numbers tend to zero at different rates. The proofs use a detailed analysis of exact and approximate fast, intermediate, and slow modes together with improved estimates for the solutions and their time derivatives, and the time-integration method. When the small parameters are related by a power law the convergence rates are positive powers of the Mach number, with the power varying depending on the component and the norm. Exceptionally, the convergence rate for two components involve the ratio of the two parameters, and that rate is proven to be sharp via corrector terms. Moreover, the convergence rates for the case of a power-law relation between the small parameters tend to the two-scale convergence rate as the power tends to one. These results demonstrate that the issue of convergence rates for three-scale singular limits, which was not addressed in the authors' previous paper, is much more complicated than for the classical two-scale singular limits.

math.AP↗

arXiv2019

Three-Scale Singular Limits of Evolutionary PDEs

Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. A simple example shows the necessity of those conditions in order for uniform bounds to hold. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero.

math.AP↗

arXiv2014

Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data

The low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space $\mathbb{R}^3$. The uniform in Mach number estimates of the solutions in a Sobolev space are obtained on a time interval independent of the Mach number. The limit is proved by using the established uniform estimates and a theorem due to Métiver and Schochet [Arch. Ration. Mech. Anal. 158 (2001), 61-90] for the Euler equations that gives the local energy decay of the acoustic wave equations.

math.AP↗

arXiv2013

Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations

We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.

math.AP↗

arXiv2012

Weak-strong uniqueness property for the compressible flow of liquid crystals

Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular direction with inhomogeneous Dirichlet boundary condition, new techniques are introduced to build up the relative entropy inequalities.

math.AP↗

arXiv2012

Low Mach number limit for the multi-dimensional Full magnetohydrodynamic equations

The low Mach number limit for the multi-dimensional full magnetohydrodynamic equations, in which the effect of thermal conduction is taken into account, is rigorously justified in the framework of classical solutions with small density and temperature variations. Moreover, we show that for sufficiently small Mach number, the compressible magnetohydrodynamic equations admit a smooth solution on the time interval where the smooth solution of the incompressible magnetohydrodynamic equations exists. In addition, the low Mach number limit for the ideal magnetohydrodynamic equations with small entropy variation is also investigated. The convergence rates are obtained in both cases.

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arXiv2011

Incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity

We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.

math.AP↗

arXiv2010

Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients and general initial data in the whole space $\mathbb{R}^d$ $ (d=2$ or 3). It is rigorously showed that, as the Mach number, the shear viscosity coefficient and the magnetic diffusion coefficient simultaneously go to zero, the weak solution of the compressible magnetohydrodynamic equations converges to the strong solution of the ideal incompressible magnetohydrodynamic equations as long as the latter exists.

math.AP↗

arXiv2010

Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.

math.AP↗

arXiv2009

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data

The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general (ill-prepared) initial data is rigorously proved in this paper. It is proved that, as the Debye length tends to zero, the solution of the compressible Navier-Stokes-Poisson system converges strongly to the strong solution of the incompressible Navier-Stokes equations plus a term of fast singular oscillating gradient vector fields. Moreover, if the Debye length, the viscosity coefficients and the heat conductivity coefficient independently go to zero, we obtain the incompressible Euler equations. In both cases the convergence rates are obtained.

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