Abstract
AbstractWe report our results [5, 6, 7] concerning a global in time unique existence theorem of strong solutions to the equation describing the motion of compressible viscous fluid flow in a 2-dimensional exterior domain for small initial data and some decay properties of the analytic semigroup associated with Stokes operator of compressible viscous fluid flow in a 2-dimensional exterior domain.Our results are an extension of the works due to Matsumura and Nishida [13] and Kobayashi and Shibata [10] in a 3-dimensional exterior domain to the 2-dimensional case.W e also discuss some analytic semigroup approach to the compressible viscous fluid flow in a bounded domain, which was first investigated by G.S trömer [20, 21, 22].Keywords2-dimensional exterior domainglobal in time unique existence theoremlocal energy decay L p-L q decay estimate
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