The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space■is rigorously proved under a Navier-slip boundary condition for velocity a...The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space■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 breakdown 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.展开更多
In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two paramete...In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.展开更多
This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infi...This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.展开更多
Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; acc...Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.展开更多
This paper is devoted to study the following dynamical system about chemical reaction with saturated output By using qualitative theory of ordinary differential equations, we have completely discussed the existence, n...This paper is devoted to study the following dynamical system about chemical reaction with saturated output By using qualitative theory of ordinary differential equations, we have completely discussed the existence, nonexistence and uniqueness of limit cycle of system (S).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12131007 and 12070144).supported by National Natural Science Foundation of China(Grant No.12001506)supported by a General Research Fund of Research Grants Council(Hong Kong)(Grant No.11306117)+1 种基金Natural Science Foundation of Shandong Province(Grant No.ZR2020QA014)supported by the Israel Science Foundation-National Natural Science Foundation of China Joint Research Program(Grant No.11761141008)。
文摘The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space■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 breakdown 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.
基金Aibin Zang was supported partially by the National Natural Science Foundation of China (11771382, 12061080, 12261093)the Jiangxi Provincial Natural Science Foundation (20224ACB201004)。
文摘In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.
基金supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005)the Tian Yuan Foundation of China(11426031)
文摘This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.
文摘Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.
文摘This paper is devoted to study the following dynamical system about chemical reaction with saturated output By using qualitative theory of ordinary differential equations, we have completely discussed the existence, nonexistence and uniqueness of limit cycle of system (S).
