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.
Bibliographical noteFunding 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 (email@example.com, firstname.lastname@example.org, email@example.com).
© 2018 Society for Industrial and Applied Mathematics.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics