A note about existence for a class of viscous fluid problems

Details A note about existence for a class of viscous fluid problems A note about existence for a class of viscous fluid problems

2012-03-30

arxiv.org/abs/1203.6799v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes the flow depends on the space variable: $q=q(\mathbf{x})$. For the associated boundary-value problem we show that, in some situations, the log-H\"older continuity condition on $q$ can be dropped and the result of the existence of weak solutions still remain valid for any variable exponent $q\geq\alpha>\frac{2N}{N+2}$, where $\alpha=\mathrm{ess}\inf q$.

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