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_{i}}\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!

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!