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On the Stokes Resolvent Equations in Locally Uniform L p Spaces in Exterior Domains

In: Functional Analysis and Evolution Equations

Author

Listed:
  • Matthias Geissert

    (TU Darmstadt, FB Mathematik)

  • Yoshikazu Giga

    (University of Tokyo, Graduate School of Mathematical Sciences)

Abstract

The Stokes resolvent equations are studied in locally uniform L p spaces where the domain is an exterior of a bounded domain. The unique existence of a solution of the Stokes resolvent equations is proved with a resolvent estimate. In particular, the analyticity of the Stokes semigroup is established. An interesting aspect of locally uniform L p spaces is that these spaces contain non-decaying functions.

Suggested Citation

  • Matthias Geissert & Yoshikazu Giga, 2007. "On the Stokes Resolvent Equations in Locally Uniform L p Spaces in Exterior Domains," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 307-314, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_20
    DOI: 10.1007/978-3-7643-7794-6_20
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