On the large time L∞-estimates of the Stokes semigroup in two-dimensional exterior domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Abe, Ken¹ 

[1] Osaka City Univ, Grad Sch Sci, Dept Math, Sumiyoshi Ku, 3-3-138 Sugimoto, Osaka 5588585, Japan

关键词: Stokes semigroup;    L-infinity-estimates;    Stokes paradox;   

DOI  :  10.1016/j.jde.2021.08.007

来源: Elsevier

【 摘 要 】

We prove that the Stokes semigroup is a bounded analytic semigroup on L-sigma(infinity) of angle pi/2 for twodimensional exterior domains. This result is an end point case of the L-p -boundedness of the semigroup for p is an element of ( 1 , infinity), established by Borchers and Varnhorn (1993). The proof is based on the non-existence result of bounded steady flows (the Stokes paradox) and some asymptotic formula for the net force of the Stokes resolvent. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free