arXiv subjects

Fucai Li

Publications and source records attributed to Fucai Li.

41 records · Page 3Linked to original sources

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.

math.AP↗

arXiv2009

Quasineutral limit of the electro-diffusion model arising in Electrohydrodynamics

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.

math.AP↗