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1.
This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge groupSU(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/r
2, asr tends to infinity.Research supported in part by the NSF, Contract No. DMS-89-05205Research supported in part by the DE, Contract No. De-FG 02-88 EF 25065 相似文献
2.
We study positive solutions of the Dirichlet problem: u(x)+f(u(x))=0,xD
n
,u(x)=0,xD
n
, whereD
n
is ann-ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.Research supported in part by NSF Contract Number MCS 80-02337 相似文献
3.
One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists. 相似文献
4.
F. Finster N. Kamran J. Smoller S.-T. Yau 《Communications in Mathematical Physics》2002,230(2):201-244
The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial
data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays
in at least at the rate t
−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].
Received: 20 August 2001 / Accepted: 22 January 2002
RID="*"
ID="*"Present address: NWF I – Mathematik, Universit?t Regensburg, 93040 Regensburg, Germany.?E-mail: felix.finster@mathematik.uni-regensburg.de
RID="**"
ID="**"Research supported by NSERC grant # RGPIN 105490-1998.
RID="***"
ID="***"Research supported in part by the NSF, Grant No. DMS-0103998.
RID="****"
ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30. 相似文献
5.
6.
Rotating Fluids with Self-Gravitation in Bounded Domains 总被引:2,自引:0,他引:2
In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of state P=eS. When the domain is a ball and the angular velocity is constant, we obtain both existence and non-existence theorems, depending on the adiabatic gas constant . In addition we obtain some interesting properties of the solutions; e.g., monotonicity of the radius of the star with both angular velocity and central density. We also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is physically striking and in sharp contrast to the case of the non-rotating star. For general domains and variable angular velocities, both an existence result for the isentropic equations of state and non-existence result for the non-isentropic equation of state are also obtained.Part of this work was completed when Tao Luo was an assistant professor at the University of Michigan. Joel Smoller was supported in part by the NSF, contract number DMS-010-3998. We are grateful to the referee for his very interesting remarks and comments, which enabled a new section, Section 6, to be added in the final version of the paper. 相似文献
7.
In earlier work we constructed a class of spherically symmetric, fluid dynamical shock waves that satisfy the Einstein equations
of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure.
Our shock waves are determined by a system of ordinary differential equations that describe the matching of a Friedmann-Robertson-Walker
metric (a cosmological model for the expanding universe) to an Oppenheimer-Tolman metric (a model for the interior of a star)
across a shock interface. In this paper we derive an alternate version of these ordinary differential equations, which are
used to demonstrate that our theory generates a large class of physically meaningful (Lax-admissible) outgoing shock waves
that model blast waves in a general relativistic setting. We also obtain formulas for the shock speed and other important
quantities that evolve according to the equations. The resulting formulas are important for the numerical simulation of these
solutions.
(Accepted January 19, 1996) 相似文献
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