I have been working with some mathematical models in biology and fluid mechanics. My problem is about
the interpretation of a condition that I found for a vector
representing the velocity of a fluid. The exact question is the next:


  Let $\mathbf{u=(}u_{1},u_{2},u_{3})$ be a vector field representing the
velocity of a fluid. After making some accounts with models using partial
differential equations, I found that the matrix
\begin{equation}
-A:=\frac{1}{2}\left(  \frac{\partial u^{j}}{\partial x_{i}}+\frac{\partial
u^{i}}{\partial x_{j}}\right)  _{i,j=1,2,3}%
\
\end{equation}
should be positive definite. Does this condition has a physical interpretation
in fluid dynamics or tensors?


Any comment or reference will be highly appreciate!