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We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a
incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical
systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the
downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed
to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results
to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations
a clearly compatible with the existence of such a solution.
Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35
Supported in part by the Fonds National Suisse. 相似文献
146.
A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle
of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference
(OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted
through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial
angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer
achieves a measurement repeatability of 10−8 rad. 相似文献
147.
148.
149.
Summary Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied
dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The
results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates.
Received 11 March 1997; accepted for publication 18 March 1998 相似文献
150.
Anita Mareno 《Journal of Mathematical Analysis and Applications》2008,343(2):932-937
This paper focuses on a nonlinear equation from thin plate theory of the form Δ(D(x)Δw)−(1−ν)[D,w]+c(x)f(w)=0. We obtain maximum principles for certain functions defined on the solution of this equation using P-functions or auxiliary functions of the types used by Payne [L.E. Payne, Some remarks on maximum principles, J. Anal. Math. 30 (1976) 421-433] and Schaefer [P.W. Schaefer, Solution, gradient, and laplacian bounds in some nonlinear fourth order elliptic equations, SIAM J. Math. Anal. 18 (1987) 430-434]. 相似文献