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On the Galerkin-Method in Intermediate Spaces for the Initial Boundary-Value Problem of the Navier-Stokes Equations in two Dimensions

✍ Scribed by Michael Böhm

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
429 KB
Volume
153
Category
Article
ISSN
0025-584X

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✦ Synopsis

We consider a GALERKM scheme for the two-dimensional initial boundary-value problem (P) of the NAVIER-STOKES equations, derive a priori-estimates for the approximations in interpolation spaces between "standard spaces'' as occuring in the theory of weak solutions and obtain well-posedness of (P) with respect to the interpolation spaces. As a by-product, we obtain various estimates for the solutions in a relatively simple way. The main tool is interpolation of non-linear operators.

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