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Existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid

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Abstract

We are concerned with the existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid in \({{\mathbb {R}}}^3\). We construct weak solutions for \(q>8/5\), and furthermore, in case \(q\ge 5/2\), we prove the existence of strong solutions.

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Acknowledgements

We thank an anonymous referee for his/her making helpful suggestion and informing the result of [5]. Kyungkeun Kang’s work is partially supported by NRF-2017R1A2B4006484 and is also supported in part by the Yonsei University Challenge of 2017. Jae-Myoung Kim’s work is supported by NRF-2015R1A5A1009350 and NRF-2016R1D1A1B03930422.

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Authors and Affiliations

  1. Department of Mathematics, Yonsei University, Seoul, Republic of Korea

    Kyungkeun Kang

  2. Center for Mathematical Analysis and Computation, Yonsei University, Seoul, Republic of Korea

    Jae-Myoung Kim

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  1. Kyungkeun Kang
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Correspondence to Jae-Myoung Kim.

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Kang, K., Kim, JM. Existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid. Nonlinear Differ. Equ. Appl. 26, 11 (2019). https://doi.org/10.1007/s00030-019-0557-7

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