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	Ill-posedness for the Navier-Stokes equations in critical Besov spaces (B) over dot(infinity,q) (-1)
	Wang, Baoxiang
	2015
关键词	Navier-Stokes equations Critical Besov spaces Ill-posedness MODULATION SPACES WEAK SOLUTIONS REGULARITY NLS
英文摘要	We study the Cauchy problem for the incompressible Navier-Stokes equations in two and higher spatial dimensions u(t) - Delta u + u .del u + del p = 0, div u = 0, u(0, x) = delta u(0). (0.1) For arbitrarily small delta > 0, we show that the solution map delta u(0) -> u in critical Besov spaces (B) over dot(infinity,q)(-1) (for all q is an element of [1,2]) is discontinuous at origin. It is known that the Navier-Stokes equation is globally well-posed for small data in BMO-1 [20]. Taking notice of the embedding (B) over dot(infinity,q)(-1) subset of BMO-1 (q <= 2), we see that for sufficiently small delta > 0, u(0) is an element of(B) over dot(infinity,q)(-1) (q <= 2) can guarantee that (0.1) has a unique global solution in BMO-1, however, this solution is instable in (B) over dot(infinity,q)(-1) and the solution can have an inflation in (B) over dot(infinity,q)(-1) for certain initial data. (C) 2014 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 0; ARTICLE; wbx@math.pku.edu.cn; 350-372; 268
语种	英语
出处	SCI
出版者	数学进展
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314204]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wang, Baoxiang. Ill-posedness for the Navier-Stokes equations in critical Besov spaces (B) over dot(infinity,q) (-1). 2015-01-01.

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