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

Tongkeun Chang, Hi Jun Choe, Kyungkeun Kang

Research output: Contribution to journalArticle

Abstract

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
Volume50
Issue number3
DOIs
Publication statusPublished - 2018 Jan 1

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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