Existence and temporal decay of regular solutions to non-Newtonian fluids combined with Maxwell equations

Hwa Kil Kim; Kyungkeun Kang; Jae Myoung Kim

doi:10.1016/j.na.2018.10.011

Existence and temporal decay of regular solutions to non-Newtonian fluids combined with Maxwell equations

Hwa Kil Kim, Kyungkeun Kang, Jae Myoung Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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 H^l-norms of the global regular solution decay with the rate of [Formula presented] for l≥0, as time tends to infinity.

Original language	English
Pages (from-to)	284-307
Number of pages	24
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	180
DOIs	https://doi.org/10.1016/j.na.2018.10.011
Publication status	Published - 2019 Mar

Bibliographical note

Funding 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 .

Funding 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.

Publisher Copyright:
© 2018 Elsevier Ltd

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2018.10.011

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title = "Existence and temporal decay of regular solutions to non-Newtonian fluids combined with Maxwell equations",

abstract = "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.",

author = "Kim, {Hwa Kil} and Kyungkeun Kang and Kim, {Jae Myoung}",

note = "Funding Information: Hwa Kil Kim{\textquoteright}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{\textquoteright}s work is supported by NRF - 2015R1D1A1A01056696 , NRF - 2018R1D1A1B07049357 and 2018 Hannam University Research Fund. Jae-Myoung Kim{\textquoteright}s work is supported by NRF - 2015R1A5A1009350 and NRF - 2016R1D1A1B03930422 . Funding 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. Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2019",

month = mar,

doi = "10.1016/j.na.2018.10.011",

language = "English",

volume = "180",

pages = "284--307",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

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AU - Kang, Kyungkeun

AU - Kim, Jae Myoung

N1 - Funding 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 . Funding 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. Publisher Copyright: © 2018 Elsevier Ltd

PY - 2019/3

Y1 - 2019/3

N2 - 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.

AB - 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.

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JO - Nonlinear Analysis, Theory, Methods and Applications

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ER -

Existence and temporal decay of regular solutions to non-Newtonian fluids combined with Maxwell equations

Abstract

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