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Tadie 《Potential Analysis》1996,5(1):61-72
Résumé Le but de cet article est d'estimer la capacité d'un pétit segment [a(1–), a(1+)]×{z=0} du démi-plan := {x = (r, z)|r > 0, z } de 2 par rapport à la capacité définie par la norme
. Ce résultat est ensuite utilisé pour estimer le diamètre de la surface libre de certains problèmes elliptiques non linéaires. 相似文献
2.
Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains
Tadie 《Applications of Mathematics》1999,44(1):1-13
In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder (rd) where (r, , z) denotes the cylindrical co-ordinates in 3 is considered. The motion is with swirl (i.e. the -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. [9] that for the problem without swirl (f
q = 0 in (f)) in the whole space, as the flux constant k tends to 1) dist(0z, A) = O(k
1/2); diam A = O(exp(–c
0
k
3/2));2) k1/2)k converges to a vortex cylinder U
m (see (1.2)).We show that for the problem with swirl, as k , 1) holds; if m q + 2 then 2) holds and if m > q + 2 it holds with U
q+2 instead of U
m. Moreover, these results are independent of f
0, f
q and d > 0. 相似文献
3.
Tadie 《Potential Analysis》1998,9(1):83-89
In this note we show that for f C((0,); R+) C1 ((0,)) with support in [0,), if a function u C1(R2) is such that support (u+) is compact and u(x) = R2 f(u(y)) log 1/(|x-y|)dy x, then u is radial. This result is important for some free boundary problems in R2 or some axisymmetric ones in Rn. 相似文献
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