Uniqueness and nonuniqueness of the Stokes and Oseen flows

被引：0
|
作者：
R. B. Guenther
E. L. Roetman
机构：
[1] Oregon State University,Department of Mathematics
[2] Embry-Riddle Aeronautical University,The Boeing Co. (Ret.)
来源：
Journal of Fixed Point Theory and Applications | 2013年 / 13卷
关键词：
76D07; 35E15; 35Q30; Stokes and Oseen flows; Cauchy problems; uniqueness classes; nonuniqueness;
D O I：
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中图分类号：
学科分类号：
摘要：
The uniqueness class for the solutions to the Cauchy problem for flows modeled by the time-dependent Stokes and Oseen systems of equations is determined as in the growth class C exp(α|x|2). An example of a type considered by Tychonoff [Mat. Sb. 42 (1935), 199–216] is given that establishes the lack of uniqueness for such Stokes and Oseen systems. Even for the incompressible Navier–Stokes system, an example shows that rapidly growing nonphysical mathematical solutions exist.
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页码：519 / 527
页数：8
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