Global well-posedness of 33-D anisotropic Navier-Stokes system with small unidirectional derivative

In \cite{LZ4}, the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical Navier-Stokes system has a global unique solution. The goal of this paper is to extend this type of result to the 3-D anisotropic Navier-Stokes system $(ANS)$ with only horizontal dissipation. More precisely, given initial data u_0=(u_0^\h,u_0^3)\in \cB^{0,\f12}, $(ANS)$ has a unique global solution provided that |D_\h|^{-1}\pa_3u_0 is sufficiently small in the scaling invariant space $\cB^{0,\f12}.

On the existence and structures of almost axisymmetric solutions to 3-D Navier-Stokes equations

In this paper, we consider 3-D Navier-Stokes equations with almost axisymmetric initial data, which means that by writing $u_0 =u^r_0 e_r+u^\theta_0 e_\theta+u^z_0 e_z$ in the cylindrical coordinates, then $\partial_\theta u^r_0,\,\partial_\theta u^\theta_0$ and $\partial_\theta u^z_0$ are small in some sense (recall axisymmetric means these three quantities vanish). Then with additional smallness assumption on $u^\theta_0$, we prove the global existence of a unique strong solution $u$, and this solution keeps close to some axisymmetric vector field. We also establish some refined estimates for the integral average in $\theta$ variable for $u$. Moreover, as $u^r_0,\,u^\theta_0$ and $u^z_0$ here depend on $\theta$, it is natural to expand them into Fourier series in $\theta$ variable. And we shall consider one special form of $u_0$, with some small parameter $\varepsilon$ to measure its swirl part and oscillating part. We study the asymptotic expansion of the corresponding solution, and the influences between different profiles in the asymptotic expansion. In particular, we give some special symmetric structures that will persist for all time. These phenomena reflect some features of the nonlinear terms in Navier-Stokes equations

Does Firm-Level Political Risk Affect Mergers and Acquisitions?

In this study I examine how a firm’s exposure to political risk affects its merger & acquisition (M&A) activities. Consistent with the predictions from real options theory, I find that a firm is less likely to engage in M&A activities and less likely to take large M&A deals when its exposure to political risk is high. This effect is particularly evident when acquirers are taking diversified M&As or when acquirers are influential and dominant in their industry. I also find a positive relationship between the time to deal completion and the acquirer’s exposure to political risk. Additionally, given that prudence and conservatism are motivated by a higher-level of political risk, I show that this leads to acquirers paying lower bid premiums and experiencing a larger increase in shareholder value from M&A deals.Thesis (MPhil) -- University of Adelaide, Adelaide Business School, 202