Functional Analytic Methods for
Evolution Systems
By: Joseph W. Jerome
By using
two prototypical applications, the hydrodynamic-Maxwell system and
the Navier-Stokes/charge transport system,
we discuss the current relevance of local smooth theories for the Cauchy
problem
based on semigroup methods, and inspired by the Friedrichs and Kato
inequalities. There appear to be three major advantages to the use of this
theory: stability under the vanishing of diffusion or viscosity
terms; flexibility in
handling block systems, which are only partially symmetrizable; the use of
implicit semidiscretization to determine estimates relating the size of
the initial datum and the admissible terminal time.
This review paper
has appeared in Contemporary Mathematics, volume 371, pp. 193--204, and
can be viewed in the following format: