6,225 research outputs found
Time-Dependent Scalar Fields in Modified Gravities in a Stationary Spacetime
Most no-hair theorems involve the assumption that the scalar field is
independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the
existence of time-dependent scalar hair outside a stationary black hole in
general relativity was ruled out. We generalize this work to modified gravities
and non-minimally coupled scalar field with an additional assumption that the
spacetime is axisymmetric. It is shown that in higher-order gravity such as
metric gravity the time-dependent scalar hair doesn't exist. While in
Palatini gravity and non-minimally coupled case the time-dependent
scalar hair may exist.Comment: 6 pages, no figure
Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles
We establish the existence and uniqueness of smooth solutions with large
vorticity and weak solutions with vortex sheets/entropy waves for the steady
Euler equations for both compressible and incompressible fluids in arbitrary
infinitely long nozzles. We first develop a new approach to establish the
existence of smooth solutions without assumptions on the sign of the second
derivatives of the horizontal velocity, or the Bernoulli and entropy functions,
at the inlet for the smooth case. Then the existence for the smooth case can be
applied to construct approximate solutions to establish the existence of weak
solutions with vortex sheets/entropy waves by nonlinear arguments. This is the
first result on the global existence of solutions of the multidimensional
steady compressible full Euler equations with free boundaries, which are not
necessarily small perturbations of piecewise constant background solutions. The
subsonic-sonic limit of the solutions is also shown. Finally, through the
incompressible limit, we establish the existence and uniqueness of
incompressible Euler flows in arbitrary infinitely long nozzles for both the
smooth solutions with large vorticity and the weak solutions with vortex
sheets. The methods and techniques developed here will be useful for solving
other problems involving similar difficulties.Comment: 43 pages; 2 figures; To be published in Advances in Mathematics
(2019
New additive results for the generalized Drazin inverse
AbstractIn this paper, we investigate additive properties of generalized Drazin inverse of two Drazin invertible linear operators in Banach spaces. Under the commutative condition of PQ=QP, we give explicit representations of the generalized Drazin inverse (P+Q)d in term of P, Pd, Q and Qd. We consider some applications of our results to the perturbation of the Drazin inverse and analyze a number of special cases
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