Abstract.
We establish partial regularity for solutions
to systems modeling electro-rheological
fluids in the stationary case. As a model case our result covers the low order regularity of systems of the type
where 
denotes the symmetric part of the gradient 
, 
denotes the pressure, the not necessarily continuous coefficient 
is a bounded non-negative
-function and the variable exponent function 
fulfills the logarithmic continuity assumption,
i.e., we assume that for the modulus of continuity 
of the exponent function 
there holds
To be more precise, we prove Hölder continuity of the
solution 
outside of a negligible set. Moreover, we show that 
and the pressure belong to certain Morrey spaces
on the regular set of 
, i.e., the set where 
is Hölder continuous. Note that under such weak assumptions partial Hölder continuity for
the gradient cannot be expected. Our result is even new if the coefficient 
is continuous.
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