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### Open Access Journals

DCDS

We study the limit of vanishing ratio of the electron mass to the
ion mass (zero-electron-mass limit) in the scaled Euler-Poisson
equations. As the first step of this justification, we construct the
uniform global classical solutions in critical Besov spaces with the
aid of ``Shizuta-Kawashima" skew-symmetry. Then we establish
frequency-localization estimates of Strichartz-type for the equation
of acoustics according to the semigroup formulation. Finally, it is
shown that the uniform classical solutions converge towards that of
the incompressible Euler equations (for

*ill-prepared*initial data) in a refined way as the scaled electron-mass tends to zero. In comparison with the classical zero-mach-number limit in [7,23], we obtain different dispersive estimates due to the coupled electric field.
CPAA

This paper is concerned with the global well-posedness and stability
of classical solutions to the Cauchy problem for the multidimensional
full hydrodynamic model in semiconductors on the framework of Besov space.
By using the high- and low- frequency decomposition method, we obtain the
exponential decay of classical solutions (close to equilibrium). Moreover, it is
also shown that the vorticity decays to zero exponentially in the 2D and 3D
space. The work

*weakens*the regularity requirement of the initial data and improves some known results in Sobolev space.
DCDS

This paper deals with non-isentropic hydrodynamic models for
semiconductors with short momentum and energy relaxation times. With
the help of the Maxwell iteration, we construct a new approximation
and show that periodic initial-value problems of certain scaled
non-isentropic hydrodynamic models have unique smooth solutions in a
time interval independent of the two relaxation times. Furthermore,
it is proved that as the two relaxation times both tend to zero, the
smooth solutions converge to solutions of the corresponding
semilinear drift-diffusion models.

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