On maximum modulus estimates of the navier–stokes equations with nonzero boundary data

Tongkeun Chang, Hi Jun Choe, Kyungkeun Kang

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1 Citation (Scopus)


We consider discontinuous influx for the Navier–Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension larger than or equal to two. This is an extension of the result in [T. Chang and H. Choe, J. Differential Equations, 254 (2013), pp. 2682–2704] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. If the normal component of bounded boundary data is Dini-continuous in space or log-Dini-continuous in time, then the constructed solution becomes bounded and a maximum modulus estimate is valid.

Original languageEnglish
Pages (from-to)3147-3171
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Issue number3
Publication statusPublished - 2018

Bibliographical note

Funding Information:
∗Received by the editors October 17, 2017; accepted for publication (in revised form) April 6, 2018; published electronically June 19, 2018. http://www.siam.org/journals/sima/50-3/M115256.html Funding: The work of the first author was supported by 2017R1D1A1B03033427. The work of the second author was supported by NRF-2015R1A5A1009350. The work of the third author was supported by NRF-2017R1A2B4006484. †Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120-749, South Korea (chang7357@yonsei.ac.kr, choe@yonsei.ac.kr, kkang@yonsei.ac.kr).

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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