an:02211008
Zbl 1088.35048
Enomoto, Yuko; Shibata, Yoshihiro
Local energy decay of solutions to the Oseen equation in the exterior domains
EN
Indiana Univ. Math. J. 53, No. 5, 1291-1330 (2004).
00112059
2004
j
35Q35 35B40 76D03 35M20
Oseen equation; \(L^p\)-\(L^q\) estimate; exterior domain; local energy decay; existence; Navier-Stokes equation
The authors prove a local energy decay of the Oseen semigroup in the \(n\)-dimensional exterior domain \((n\geq 3)\). To formulate the Oseen equation in the framework of semigroup theory, the authors introduce the Helmholtz decomposition. The local energy decay is a crucial step to obtain \(L^p\)-\(L^q\) estimates of the Oseen semigroup, which in turn enables to prove the unique existence of global in time solutions to the Navier-Stokes equation in an exterior domain with small initial data in the \(L_m\) framework, and their properties of time decay.
Messoud A. Efendiev (Berlin)