The 6th PDE Real Analysis Seminar
(COE Partner Seminar, Department of Mathematics, Hokkaido University )
Outline
- Organizers :
- H.Arai (University of Tokyo), Y. Giga (Hokkaido University)
- Period :
- January 26, 2005 (Wednesday)
- Place :
- Graduate School of Mathematical Sciences the University of Tokyo, Room #122
- Programme :
-
- Matthias Hieber (TU Darmstadt)
- "L^p-Theory of the Navier-Stokes flow past rotating or moving obstacles"
- ABSTRACT:
- In this talk we consider the equation of Navier-Stokes in the exterior of
a rotating or moving domain. Using techniques from the analysis of
Ornstein-Uhlenbeck operators it is shown that, after rewriting the problem
on a fixed domain $\Omega$, the solution of the linearized equation is
governed by a $C_0$-semigroup on $L^p_\sigma(\Omega)$ for $1<p<\infty$
with generator $Au=P(\Delta u +Mx\cdot \nabla u - Mu)$.
Moreover, for $p\geq n$ and initial data $u_0 \in L^p_\sigma(\Omega)$ we
prove the existence of a unique local mild solution of the Navier-Stokes
problem.
