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The A-Stokes approximation for non-stationary problems
Let be an elliptic tensor. A function
is a solution to the non-stationary -Stokes problem iff
\begin{align}\label{abs} \int_Q v\cdot\partial_t\phi\,dx\,dt-\int_Q \mathcal
A(\varepsilon(v),\varepsilon(\phi))\,dx\,dt=0\quad\forall\phi\in
C^{\infty}_{0,div}(Q), \end{align} where ,
bounded. If the l.h.s. is not zero but small we talk about almost solutions. We
present an approximation result in the fashion of the -caloric
approximation for the non-stationary -Stokes problem. Precisely,
we show that every almost solution ,
, can be approximated by a solution in the
-sense for all . So, we extend the stationary -Stokes approximation by Breit-Diening-Fuchs to parabolic problems
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