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\centerline{\large \bf A Well-Posed Cauchy Problem for the
Hydrodynamic}

\centerline{\large \bf Model: A Local Smooth Theory}

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\centerline{J.W. Jerome}
\centerline{\it Northwestern University, Evanston, USA}
\centerline{e-mail {\tt jwj@math.northwestern.edu}}

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\par
%   Text of the abstract
We study the Bl{\o}tekj{\ae}r hydrodynamic model from the standpoint of local
well-posedness. We employ analytical methods, originally introduced by
T.~Kato for complex systems,
to obtain the existence of unique local smooth solutions of the Cauchy
problem, with smooth initial data. The time interval is invariant with
respect to vanishing heat flux.
The model is self-consistent, and is developed for one-valley
electron carriers only. A symmetrizer is introduced for the system,
when expressed in nonconservative form, in terms of the electron density,
velocity, and temperature.
Regularization is employed to avoid the formation of singularities due to
vacuum regions.
In the regime studied, it is not possible for shocks to form.
The analytical formulation facilitates the analysis of the zero relaxation
limit.

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