| Abstract: |
| R. Rautmann, Paderborn University, Germany.
We consider a variant of the classical Navier-Stokes approximation schemes due to Fujita-Kato and to Giga-Miyakawa: By iterative solution of linear singular Volterra integral equations on any compact time interval $J$, in any smoothly bounded domain $\Omega \subset \RR^n$, $2 \leq n$, again we find the existence of a unique mild Navier-Stokes solution under smallness conditions, but moreover we get the stability of each (possibly large) mild solution, inside a scale of Banach spaces which are imbedded in some spaces $C^0 (J, L^r (\Omega))$, $ 1 < r < \infty$.
e-mail: rautmann@math.uni-paderborn.de |
|