Initial value problem for the free boundary magnetohydrodynamics with zero magnetic boundary condition

We show local existence and uniqueness of plasma(fluid)-vaccum free boundary problem of magnetohydrodynamic flow in three-dimensional space with infinite depth setting when magnetic field is zero on the free boundary. We use Sobolev-Slobodetskii space which was used in usual free boundary problem in [3,5,6,7,8,9]. We also show that this solution can be extended as long as we want for sufficiently small initial data. Using the result of this paper we will get a unique solution of (kinematic inviscid) - (magnetic non diffusive) free boundary magnetohydrodynamics problem via (kinematic viscosity) - (magnetic diffusivity) limit in [10].Comment: Accepted in Comm. Math. Sci. (2017

Uniform Regularity for free-boundary navier-stokes equations with surface tension

We study the zero-viscosity limit of free boundary Navier-Stokes equations with surface tension in $\mathbb{R}^3$ thus extending the work of Masmoudi and Rousset [1] to take surface tension into account. Due to the presence of boundary layers, we are unable to pass to the zero-viscosity limit in the usual Sobolev spaces. Indeed, as viscosity tends to zero, normal derivatives at the boundary should blow-up. To deal with this problem, we solve the free boundary problem in the so-called Sobolev co-normal spaces (after fixing the boundary via a coordinate transformation). We prove estimates which are uniform in the viscosity. And after inviscid limit process, we get the local existence of free-boundary Euler equation with surface tension. One of the main differences between this work and the work [1] is our use of time-derivative estimates and certain properties of the Dirichlet-Neumann operator. In a forthcoming work, we discuss how we can take the simultaneous limit of zero viscosity and surface tension [].Comment: Accepted in JHDE (2017

Invisible Trade Barriers: Trade Effects of US Antidumping Actions Against the People’s Republic of China

We conduct an empirical analysis on the impact of the United States (US) antidumping actions against the People’s Republic of China (PRC) on the bilateral trade and US imports from other trade partners. Using the data set based on the Harmonized System (HS) tariff code, we examine the trade patterns of the PRC and other countries, and find evidence for the trade restriction effect and the trade diversion effect. Further, we examine the intensity and duration of both restriction and diversion effects. The antidumping measures have effectively raised the prices of imports from the PRC and reduced US imports from the PRC only in the short term. Nevertheless, due to the coexistence of trade diversion effects, the overall remedy effect of antidumping actions on domestic industries is considerably limited. In addition, we investigate other factors that influence the efficiency of antidumping measures, such as the antidumping duty amount, the PRC’s market position in the US, and the US market share in the PRC