Applications of Mathematics, first online, pp. 1-11
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces
Yanghai Yu, Fang Liu
Received April 16, 2024. Published online October 10, 2024.
Abstract: We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from $u_0$ are discontinuous at $t = 0$.
Keywords: Navier-Stokes equation; Euler equation; ill-posedness; Besov space
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Affiliations: Yanghai Yu (corresponding author), Fang Liu, School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, P. R. China, e-mail: yuyanghai214@sina.com, lf191110@163.com
