Ill-posedness of the stationary Navier-Stokes equations in Besov spaces
Ill-posedness of the stationary Navier-Stokes equations in Besov spaces
复制标题
Besov 空间中平稳纳维-斯托克斯方程的不适定性
DOI：
10.1016/j.jmaa.2019.03.046
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发表时间：
2019
影响因子：
1.3
通讯作者：
Tsurumi Hiroyuki
中科院分区：
文献类型：
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作者：
Hiroyuki Tsurumi;Tsurumi Hiroyuki
在标度不变的Besov空间中，研究了Rn中n≥3的定常N-S方程的解.证明了B·∞，1−3范数收敛于零的有界光滑外力序列可以产生B·−1∞，∞范数永不收敛于零的有界光滑解序列.这种范数膨胀现象是通过构造外力序列来表示的，类似于Bourain-Pavlović在非平稳问题中提出的初始数据的序列。
The solutions of the stationary Navier-Stokes equations in R n for n≥ 3 in the scaling invariant Besov spaces are investigated. It is proved that a sequence of bounded smooth external forces whose B˙∞, 1− 3 norms converges to zero can produce a sequence of bounded smooth solutions whose B˙− 1∞,∞ norms never converges to zero. Such norm inflation phenomena are shown by constructing the sequence of external forces, as similar to those of initial data proposed by Bourgain-Pavlović in the non-stationary problem.