6,550 research outputs found
Incompressible Limit of Solutions of Multidimensional Steady Compressible Euler Equations
A compactness framework is formulated for the incompressible limit of
approximate solutions with weak uniform bounds with respect to the adiabatic
exponent for the steady Euler equations for compressible fluids in any
dimension. One of our main observations is that the compactness can be achieved
by using only natural weak estimates for the mass conservation and the
vorticity. Another observation is that the incompressibility of the limit for
the homentropic Euler flow is directly from the continuity equation, while the
incompresibility of the limit for the full Euler flow is from a combination of
all the Euler equations. As direct applications of the compactness framework,
we establish two incompressible limit theorems for multidimensional steady
Euler flows through infinitely long nozzles, which lead to two new existence
theorems for the corresponding problems for multidimensional steady
incompressible Euler equations.Comment: 17 pages; 2 figures. arXiv admin note: text overlap with
arXiv:1311.398
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
Income Tax and Salesforce Performance: A Micro Perspective
How does the change in income tax affect sales performance? Our paper explores the link between economic policy and salesforce management at the transactional level, using data from a large fashion retailer in China. The analysis shows that the implementation of a nationwide personal income tax cut in October 2018 improves sales performance more among those salespersons who benefited from the policy, compare to others. The performance gain is observed after the tax cut and persisted in future months, and is particularly significant in low-income regions. We also find that the performance gain is largely due to an increase in sales of pricier items, rather than more reliance on discounts. Finally, the research shows that the net effect of the tax cut is an increase in the government’s revenue due to the firm’s higher sales and corresponding increase in corporate tax paid
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