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Regularity of Non-Newtonian Fluids

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Abstract

In this paper, we consider a non-Newtonian fluids with shear dependent viscosity in a bounded domain \({\Omega \subset \mathbb{R}^n, n = 2, 3}\) . For the power-law model with the viscosity as in (1.4), we show the global in time existence of a weak solution for \({q \geq \frac{11}{5}}\) when n = 3 (see Theorem 1.1), and the local in time existence of a weak solution for \({2 > q > \frac{3n}{n+2}}\) , when n = 2,3 (see Theorem 1.2).

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Authors and Affiliations

  1. Department of Financial Engineering, Ajou Univesity, Suwon, 443-749, Republic of Korea

    Hyeong-Ohk Bae

  2. Department of Mathematics Education, Mokpo National University, Muan, 534-729, Republic of Korea

    Bum Ja Jin

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  1. Hyeong-Ohk Bae
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  2. Bum Ja Jin
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Correspondence to Bum Ja Jin.

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Communicated by H. Beirão da Veiga

This work was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology 2010-0016694.

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Bae, HO., Jin, B.J. Regularity of Non-Newtonian Fluids. J. Math. Fluid Mech. 16, 225–241 (2014). https://doi.org/10.1007/s00021-013-0149-y

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