Abstract
We prove the local regularity of a weak solution \({\varvec{u}}\) to the equations of a generalized Newtonian fluid with power law \(1< q \le 2\) if \({\varvec{u}}\) belongs to a suitable Lebesgue space. This result extends the well-known Serrin condition for weak solutions of the Navier–Stokes equations to the shear-thinning fluids.
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Dedicated to Professor Hi Jun Choe on the occasion of his 60th birthday.
Bae was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2015R1D1A1A01057976), and partially by National Institute for Mathematical Sciences (NIMS: A23100000), while Wolf was supported by the Brain Pool Project of the Korea Federation of Science and Technology Societies (141S-1-3-0022).
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Bae, HO., Wolf, J. Sufficient conditions for local regularity to the generalized Newtonian fluid with shear thinning viscosity. Z. Angew. Math. Phys. 68, 7 (2017). https://doi.org/10.1007/s00033-016-0751-y
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DOI: https://doi.org/10.1007/s00033-016-0751-y