Analyticity of the Stokes semigroup in spaces of bounded functions
By Ken Abe, Yoshikazu Giga. 2011
109 citations recorded by the source corpus.
The analyticity of the Stokes semigroup with the Dirichlet boundary condition is established in spaces of bounded functions when the domain occupied with fluid is bounded or more generally admissible which admits a special estimate for the Helmholtz decomposition. The proof is based on a blow-up argument. This is the first proof of the analyticity in spaces of bounded functions which was left open more than thirty years.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/16adfb22c92a6c1b4c33640ff528d6e6a3598756
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- The stokes equation in the Lp-setting: Well-posedness and regularity properties (2018, background): “Abe and Giga [1] proved in 2013 the following breakthrough result.”
- Stokes Resolvent Estimates in Spaces of Bounded Functions (2012, methodology): “ on explicit calculations of the solution operator R(λ) : f → v = vλ of the corresponding resolvent problem of (1.1) λv −∆v +∇q = f in Ω, (1.2) div v = 0 in Ω, (1.3) v = 0 on ∂Ω. As recently shown in [2], [3] by a blow-up argument to the non-stationary Stokes equations, it turns out that the Stokes ”