The Library
An example of finite-time singularities in the 3d Euler equations
Tools
He, Xinyu (2007) An example of finite-time singularities in the 3d Euler equations. Journal of Mathematical Fluid Mechanics, Vol.9 (No.3). pp. 398-410. doi:10.1007/s00021-005-0205-3 ISSN 1422-6928.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s00021-005-0205-3
Abstract
Let Omega = R-3\(B) over bar _1(0) be the exterior of the closed unit ball. Consider the self-similar Euler system
alpha u+beta y.del u+u.del u+del p=0, div u=0 in Omega.
Setting alpha=beta=1/2 gives the limiting case of Leray's self-similar Navier-Stokes equations. Assuming smoothness and smallness of the boundary data on partial derivative Omega, we prove that this system has a unique solution (u,p) epsilon C-1(Omega;R(3)xR), vanishing at infinity, precisely
u(y)down arrow 0 as vertical bar y vertical bar up arrow infinity, with u = O(vertical bar y vertical bar(-1)), del u=O(vertical bar y vertical bar(-2)).
The self-similarity transformation is v(x,t)=u(y)/(t*-t)(alpha), y=x/(t*-t)(beta), where v(x,t) is a solution to the Euler equations. The existence of smooth function u(y) implies that the solution v(x,t) blows up at (x*,t*), x*=0, t*<+infinity. This isolated singularity has bounded energy with unbounded L-2-norm of curl v.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics |
||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Mathematical Fluid Mechanics | ||||
Publisher: | Birkhaeuser Verlag AG | ||||
ISSN: | 1422-6928 | ||||
Official Date: | August 2007 | ||||
Dates: |
|
||||
Volume: | Vol.9 | ||||
Number: | No.3 | ||||
Number of Pages: | 13 | ||||
Page Range: | pp. 398-410 | ||||
DOI: | 10.1007/s00021-005-0205-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |