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We study error estimates and their convergence rates for approximate solutions of spectral Galerkin type for the equations for the motion of a viscous chemical active fluid in a bounded domain. We find error estimates that are uniform in time and also optimal in the L2-norm and H1-norm. New estimates in the H(-1)-norm are given.
By using the spectral Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type in non-cylindrical domains.
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