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

Hwa Kil Kim, Kyungkeun Kang, Jae Myoung Kim

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)284-307
Number of pages24
JournalNonlinear Analysis, Theory, Methods and Applications
Volume180
DOIs
Publication statusPublished - 2019 Mar 1

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Regular Solution
Non-Newtonian Fluid
Maxwell equations
Maxwell's equations
Decay
Fluids
Norm
Fourier Method
Splitting Method
Local Existence
Three-dimension
Cauchy Problem
Infinity
Tend

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Existence and temporal decay of regular solutions to non-Newtonian fluids combined with Maxwell equations. / Kim, Hwa Kil; Kang, Kyungkeun; Kim, Jae Myoung.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 180, 01.03.2019, p. 284-307.

Research output: Contribution to journalArticle

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