A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing

  title={A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing},
  author={Miroslav Bul{\'i}{\vc}ek and Jan Burczak and Sebastian Schwarzacher},
  journal={SIAM J. Math. Anal.},
We consider a model of steady, incompressible non-Newtonian flow with neglected convective term under external forcing. Our structural assumptions allow for certain nondegenerate power-law or Carreau-type fluids. Within our setting, we provide the full-range theory, namely, existence, optimal regularity, and uniqueness of solutions, not only with respect to forcing belonging to Lebesgue spaces, but also with respect to their refinements, namely, the weighted Lebesgue spaces, with weights in a… 
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