On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-slip Boundary Conditions

In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded smooth domain of $R^3$ with the generalized Navier-slip boundary conditions (\ref{VSg}). Some uniform estimates on rates of convergence in $C([0,T],L^2(\Omega))$ and $C([0,T],H^1(\Omega))$ of the solutions to the corresponding solutions of the idea Euler equations with the standard slip boundary condition are obtained

Branching ratios of Bc→APB_c \to A P decays in the perturbative QCD approach

In this paper we calculate the branching ratios (BRs) of the 32 charmless hadronic $B_c \to A P$ decays ($A=a_1(1260),b_1(1235),K_1(1270),K_1(1400), f_1(1285),f_1(1420),h_1(1170),h_1(1380)$) by employing the perturbative QCD(pQCD) factorization approach. These considered decay channels can only occur via annihilation type diagrams in the standard model. From the numerical calculations and phenomenological analysis, we found the following results: (a) the pQCD predictions for the BRs of the considered $B_c$ decays are in the range of $10^{-6}$ to $10^{-8}$, while the CP-violating asymmetries are absent because only one type tree operator is involved here; (b) the BRs of $\Delta S= 0$ processes are generally much larger than those of $\Delta S =1$ ones due to the large CKM factor of $|V_{ud}/V_{us}|^2\sim 19$; (c) since the behavior for $^1P_1$ meson is much different from that of $^3P_1$ meson, the BRs of $B_c \to A(^1P_1) P$ decays are generally larger than that of $B_c \to A(^3P_1) P$ decays; (d) the pQCD predictions for the BRs of B_c \to (K_1(1270), K_1(1400)) \etap and $(K_1(1270), K_1(1400)) K$ decays are rather sensitive to the value of the mixing angle $\theta_K$.Comment: 1+17 pges, 1 figure, refs. added and some clarifications made, accepted for publication in Phys.Rev.