We consider the Cauchy problem of a certain type of non-Newtonian fluids combined with Maxwell equations in three dimensions. We establish local existence of unique regular solutions for sufficiently smooth initial data. In addition, the regular solutions are globally extended in time, provided that the H3-norm of the initial data is small enough. Lastly, using the Fourier splitting method, we show that Hl-norms of the global regular solution decay with the rate of [Formula presented] for l≥0, as time tends to infinity.
|Number of pages||24|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2019 Mar|
Bibliographical noteFunding Information:
Hwa Kil Kim’s work is partially supported by NRF - 2017R1A2B4006484 and NRF - 2015R1A5A1009350 and is supported in part by the Yonsei University Challenge of 2017. Kyungkeun Kang’s work is supported by NRF - 2015R1D1A1A01056696 , NRF - 2018R1D1A1B07049357 and 2018 Hannam University Research Fund. Jae-Myoung Kim’s work is supported by NRF - 2015R1A5A1009350 and NRF - 2016R1D1A1B03930422 .
All Science Journal Classification (ASJC) codes
- Applied Mathematics