On some decay properties of Stokes semigroup of compressible viscous fluid flow in a 2-dimensional exterior domain

详细信息	查看全文 | 推荐本文 |

• 作者：Yuko Enomoto^a ; ^{e-yuko@shibaura-it.ac.jp} ; Yoshihiro Shibata^b
• 关键词：Stokes semigroup ; Compressible viscous fluid ; 2-dimensional exterior domain ; Local energy decay ; Lp&ndash ; Lq decay
• 刊名：Journal of Differential Equations
• 出版年：2012
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：15 June, 2012
• 卷：252
• 期：12
• 页码：6214-6249
• 文件大小：407 K

摘要

In this paper, we proved the local energy decay and some - decay properties of solutions to the initial-boundary value problem for the Stokes equations of compressible viscous fluid flow in a 2-dimensional exterior domain. Kobayashi (1997) and Kobayashi and Shibata (1999) treated the same problem in a 3-dimensional exterior domain, and our results obtained in this paper are an extension of results in Kobayashi (1997) and Kobayashi and Shibata (1999) to the 2-dimensional case. The fundamental solution to the resolvent equations for the Stokes equations in has a logarithmical singularity at , 位 being a resolvent parameter, while it is continuous up to in . This difference requires us a new idea to prove the local energy decay estimate. Once getting the local energy decay estimate, the required - decay estimates in the exterior domain are obtained by combining the local energy estimate and the - estimates in by a cut-off technique.