Stokes Resolvent Estimates in Spaces of Bounded Functions

By Ken Abe, Yoshikazu Giga, Matthias Hieber. 2012

53 citations recorded by the source corpus.

We give a direct proof for the analyticity of the Stokes semigroup in spaces of bounded functions. This was recently proved by an indirect argument by the first and second authors for a class of domains called strictly admissible domains including bounded and exterior domains. Invoking the strictly admissibility, our approach is based on an adjustment of a standard resolvent estimate method for general elliptic operators introduced by K. Masuda (1972) and H. B. Stewart (1974). The resolvent approach in particular clarifies the sectorial region, Re z > 0 for z ∈ C for which the Stokes semigroup has an analytic continuation in spaces of bounded functions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e0d58a5addde41f255f7bc7545a8d99ebf80fe4f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ken Abe
2. Yoshikazu Giga

In Computational Theory and Mathematics

1. Ken Abe
2. Yoshikazu Giga
3. Matthias Hieber

In Mathematical Physics

1. Ken Abe
2. Yoshikazu Giga
3. Matthias Hieber

Citations in the corpus

• Analyticity of the Stokes semigroup in spaces of bounded functions (2011, background): “Hieber and the authors [2] found a way to prove Theorem 1.”
• The L∞-Stokes semigroup in exterior domains (2012, methodology): “Although we recently found a way to prove the analyticity of the Stokes semigroup on L∞-type spaces via a resolvent estimate [2], our approach in this paper gives an a priori estimate for higher derivatives which does not follow from a resolvent estimate in a direct way.”