Navier Boundary Condtion for Stokes equation

I am learning the document written by Prof. Frederic Hecht on boundary conditions for the Stokes equation.

I have a question about the Navier boundary condition. How the following equation is derived, especially the negative symbol?

Thank you.

@frederichecht professor, I try to derive the above identity (see the following figure). I have two questions: (1) in your side term \mathbf{\tau} \cdot \mathbf{v} is dropped for \mathbf{g}\cdot \mathbf{\tau}, it’s a typo or I missing something?
(2) could you kindly tell me why the term marked in blue (the normal component, see the following figure) is dropped?

It is a Typo all term g.\tau must be multiplie by v so get g.\tau. v == (g.\tau).( v.\tau)

Dear Prof. Frédéric Hecht‬,
Thanks for your kind reply. Could you kindly tell me why the term \int \left( \mathbf{f}_\Gamma\cdot\mathbf{n} \right) \left( \mathbf{n} \cdot \mathbf{v}\right) \text{d}\Gamma is dropped? Thanks in advance.



because I miss this term, sorry.

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Professor, thanks for your kind reply