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In this paper, we perform analysis of the fluid velocity vector field divergence $\nabla \cdot \vec{u}$ derived from the continuity equation, and we explore its application in the Navier-Stokes equations for compressible fluids $\rho (\vec{x},t)\ne const$, occupying all of $\vec{x}\in R^{3} $ space at any $t\geq 0$. The resulting velocity vector field divergence $\nabla \cdot \vec{u}=-\frac{1}{\rho } (\frac{\partial \rho }{\partial t} +\vec{u}\cdot \nabla \rho )$ is a direct consequence of the fluid density rate of change over time $\frac{\partial \rho }{\partial t}$ and over space $\nabla \rho $, in addition to the fluid velocity vector field $\vec{u}(\vec{x},t)$ and the fluid density $\rho (\vec{x},t)$ itself. We derive the conditions for the divergence-free fluid velocity vector field $\nabla \cdot \vec{u}=0$ in scenarios when the fluid density is not constant $\rho(\vec{x},t)\neq const$ over space nor time, and we analyze scenarios of the non-zero divergence $\nabla \cdot \vec{u}\ne 0$. We apply the statement for divergence in the Navier-Stokes equation for compressible fluids, and we deduct the condition for vanishing (zero) viscosity term of the compressible Navier-Stokes equation: $\nabla (\frac{1}{\rho } (\frac{\partial \rho }{\partial t} +\vec{u}\cdot \nabla \rho ))=-3\Delta \vec{u}$. In addition to that, we derive even more elementary condition for vanishing viscosity, stating that vanishing viscosity is triggered once scalar function $d(\vec{x},t)=-\frac{1}{\rho } (\frac{\partial \rho }{\partial t} +\vec{u}\cdot \nabla \rho )$ is harmonic function. Once that condition is satisfied, the viscosity related term of the Navier-Stokes equations for compressible fluids equals to zero, which is known as related to turbulent fluid flows., Comment: 13 pages

We provide an example of a smooth, divergence-free $\nabla \cdot \vec{u}(\vec{x})=0$ velocity vector field $\vec{u}(\vec{x})$ for incompressible fluid occupying all of $R^{3}$ space, and smooth vector field $\vec{f}(\vec{x}, t)$ for which the Navier-Stokes equation for incompressible fluid does not have a solution for any position in space $\vec{x}\in R^{3} $ at $t=0$. The velocity vector field $u_{i} (\vec{x})=2\frac{x_{h(i-1)} -x_{h(i+1)} }{\left(1+\sum _{j=1}^{3}x_{j}^{2} \right)^{2} }$ ; $i=\{ 1,2,3\} $ where $h(l)=\left\{\begin{array}{ccc} {l} & {;1\le l\le 3} & {} \\ {1} & {;l=4} & {} \\ {3} & {;l=0} & {} \end{array}\right.$ is smooth, divergence-free, continuously differentiable $u(\vec{x})\in C^{\infty }$, has bounded energy $\int _{R^{3} }\left|\vec{u}\right|^{2} dx=��^{2}$, zero velocity at coordinate origin, and velocity converges to zero for $\left|\vec{x}\right|\to \infty$. The vector field $\vec{f}(\vec{x},t)=(0,0,\frac{1}{1+t^{2} (\sum _{j=1}^{3}x_{j} )^{2} )} $ is smooth, continuously differentiable $f(\vec{x},t)\in C^{\infty }$, converging to zero for $\left|\vec{x}\right|\to \infty$. Applying $\vec{u}(\vec{x})$ and $\vec{f}(\vec{x}, t)$ in the Navier-Stokes equation for incompressible fluid results with three mutually different solutions for pressure $p(\vec{x}, t)$, one of which includes zero division with zero $\frac{0}{0}$ term at $t=0$, which is indeterminate for all positions $\vec{x} \in R^{3}$.

In this paper, we perform analysis of the fluid velocity vector field divergence $\nabla \cdot \vec{u}$ derived from the continuity equation, and we explore its application in the Navier-Stokes equations for compressible fluids $��(\vec{x},t)\ne const$, occupying all of $\vec{x}\in R^{3} $ space at any $t\geq 0$. The resulting velocity vector field divergence $\nabla \cdot \vec{u}=-\frac{1}{��} (\frac{\partial ��}{\partial t} +\vec{u}\cdot \nabla ��)$ is a direct consequence of the fluid density rate of change over time $\frac{\partial ��}{\partial t}$ and over space $\nabla ��$, in addition to the fluid velocity vector field $\vec{u}(\vec{x},t)$ and the fluid density $��(\vec{x},t)$ itself. We derive the conditions for the divergence-free fluid velocity vector field $\nabla \cdot \vec{u}=0$ in scenarios when the fluid density is not constant $��(\vec{x},t)\neq const$ over space nor time, and we analyze scenarios of the non-zero divergence $\nabla \cdot \vec{u}\ne 0$. We apply the statement for divergence in the Navier-Stokes equation for compressible fluids, and we deduct the condition for vanishing (zero) viscosity term of the compressible Navier-Stokes equation: $\nabla (\frac{1}{��} (\frac{\partial ��}{\partial t} +\vec{u}\cdot \nabla ��))=-3��\vec{u}$. In addition to that, we derive even more elementary condition for vanishing viscosity, stating that vanishing viscosity is triggered once scalar function $d(\vec{x},t)=-\frac{1}{��} (\frac{\partial ��}{\partial t} +\vec{u}\cdot \nabla ��)$ is harmonic function. Once that condition is satisfied, the viscosity related term of the Navier-Stokes equations for compressible fluids equals to zero, which is known as related to turbulent fluid flows., 13 pages

The paper investigates transmission of different foreign and domestic shocks to bank lending activity in Bosnia and Herzegovina through the bank lending channel. The bank lending channel is analyzed in a time series cross sectional data framework for the period 2006q1-2014q1, investigating reactions of small vs. large banks to those shocks. First, the evidence has been found that both groups of banks decreased their lending activity in the aftermath of the crisis. There is some evidence that liquidity shock after the onset of the crisis is mainly transmitted through large banks that are affiliates of the large Western European banking groups. Second, strong evidence is found that loosening of domestic monetary conditions through required reserves rate change had a positive effect on lending supply, especially for small banks operating in the country.