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Search Results: 1 - 10 of 127153 matches for " Fucai Li "
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Quasineutral limit of the electro-diffusion model arising in Electrohydrodynamics
Fucai Li
Mathematics , 2009,
Abstract: The electro-diffusion model, which arises in electrohydrodynamics, is a coupling between the Nernst-Planck-Poisson system and the incompressible Navier-Stokes equations. For the generally smooth doping profile, the quasineutral limit (zero-Debye-length limit) is justified rigorously in Sobolev norm uniformly in time. The proof is based on the elaborate energy analysis and the key point is to establish the uniform estimates with respect to the scaled Debye length.
Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system
Song Jiang,Fucai Li
Mathematics , 2014, DOI: 10.1007/s11425-014-4923-y
Abstract: In this paper we investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system. We justify this singular limit rigorously in the framework of smooth solutions and obtain the non-isentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.
Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations
Song Jiang,Fucai Li
Mathematics , 2013, DOI: 10.3233/ASY-151321
Abstract: The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic approximation in physical books. In this paper we justify this singular limit rigorously in the framework of smooth solutions for well-prepared initial data.
The quasineutral limit of compressible Navier-Stokes-Poisson system with heat conductivity and general initial data
Qiangchang Ju,Fucai Li,Hailiang Li
Mathematics , 2009,
Abstract: 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.
Global Existence and Blow-up of Solutions to a Quasi-linear Degenerate Parabolic System
拟线性退化抛物型方程组解的整体存在性和爆破

Li Fucai,
栗付才

数学物理学报(A辑) , 2008,
Abstract: 该文研究光滑有界区域Ω∩→R^N(N≥1)上具有齐次Dirichlet边界条件的拟线性退化抛物型方程组ut-div(|△u|^p-2△u)=av^α,vt-div(|△v|^q-2△v)=bu^β的非负解的性质,其中P,q〉2,α,β≥1,a,b〉0是常数.该文指出上述方程组的解是否在有限时刻爆破依赖于初值、系数a与b以及αβ和(P-1)(q-1)之间的关系.
Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions
Song Jiang,Qiangchang Ju,Fucai Li
Mathematics , 2010,
Abstract: 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.
Regularity criteria and uniform estimates for the Boussinesq system with the temperature-dependent viscosity and thermal diffusivity
Jishan Fan,Fucai Li,Gen Nakamura
Mathematics , 2012,
Abstract: In this paper we establish some regularity criteria for the 3D Boussinesq system with the temperature-dependent viscosity and thermal diffusivity. We also obtain some uniform estimates for the corresponding 2D case when the fluid viscosity coefficient is a positive constant.
Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations
Song Jiang,Qiangchang Ju,Fucai Li
Mathematics , 2013,
Abstract: 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.
Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces
Fucai Li,Yanmin Mu,Dehua Wang
Mathematics , 2014,
Abstract: The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.
Non-relativistic limit of the compressible Navier-Stokes-Fourier-P1 approximation model arising in radiation hydrodynamics
Song Jiang,Fucai Li,Feng Xie
Mathematics , 2015,
Abstract: As is well-known that the general radiation hydrodynamics models include two mainly coupled parts: one is macroscopic fluid part, which is governed by the compressible Navier-Stokes-Fourier equations, another is radiation field part, which is described by the transport equation of photons. Under the two physical approximations: "gray" approximation and P1 approximation, one can derive the so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model from the general one. In this paper we study the non-relativistic limit problem for the Navier-Stokes-Fourier-P1 approximation model due to the fact that the speed of light is much larger than the speed of the macroscopic fluid. Our results give a rigorous derivation of the widely used macroscopic model in radiation hydrodynamics.
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