About Compressible Viscous Fluid Flow in a 2-dimensional Exterior Domain
We 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  and Kobayashi and Shibata  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 domain global in time unique existence theorem local energy decay Lp-Lq decay estimate
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- 5.Y. Enomoto and Y. Shibata, On some decay properties of Stokes semigroup of compressible viscous fluid flow in a two-dimensional exterior domain, preprint.Google Scholar
- 6.Y. Enomoto, Y. Shibata and M. Suzuki, On the maximal Lp-Lq regularity of the Stokes semigroup of compressible viscous fluid flow and its application to a nonlinear problem, preprint.Google Scholar
- 7.Y. Enomoto, Y. Shibata and M. Suzuki, On the global in time unique existence theorem for the compressible viscous fluid flow in 2-dimensional exterior domains, preprint.Google Scholar
- 18.Y. Shibata and S. Shimizu, On the maximal Lp-Lq regularity of the Stokes problem with first-order boundary condition: Model Problem, to appear in J. Math. Soc. Japan.Google Scholar
- 24.B. Vainberg, Asymptotic Methods in Equations of Mathematical Physics, in Russian, Moscow Univ. Press, 1982; Gordon and Breach Publishers, New York, London, Paris, Montreux, Tokyo, 1989; English translation.Google Scholar