Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth

Hyeong-Ohk Bae; Hyoungsuk So; Yeonghun Youn; Hyeong-Ohk Bae; Hyoungsuk So; Yeonghun Youn

doi:10.3934/nhm.2018021

Networks and Heterogeneous Media

2018, Volume 13, Issue 3: 479-491. doi: 10.3934/nhm.2018021

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Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth

1.
Department of Financial Engineering, Ajou University, Suwon, Korea
2.
Manufacturing Technology Center, Samsung Electronics, Giheung, Korea
3.
Department of Mathematics, Seoul National University, Seoul 08826, Republic of Korea

Received: 01 November 2017 Revised: 01 March 2018
Primary: 35Q35; Secondary: 35B65, 76A05

We consider weak solutions to the equations of stationary motion of a class of non-Newtonian fluids which includes the power law model. The power depends on the spatial variable, which is motivated by electrorheological fluids. We prove the existence of second order derivatives of weak solutions in the shear thinning cases.
- Power-law fluid,
- strong solution,
- variable exponent space,
- shear thinning fluid,
- regularity
Citation: Hyeong-Ohk Bae, Hyoungsuk So, Yeonghun Youn. Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth[J]. Networks and Heterogeneous Media, 2018, 13(3): 479-491. doi: 10.3934/nhm.2018021

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Abstract

We consider weak solutions to the equations of stationary motion of a class of non-Newtonian fluids which includes the power law model. The power depends on the spatial variable, which is motivated by electrorheological fluids. We prove the existence of second order derivatives of weak solutions in the shear thinning cases.

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