> restart;
> with(linalg);
> uvec := array(1 .. 2, [u_(x, y, t), v_(x, y, t)]):
> xvec := array(1 .. 2, [x, y]):
> equns := array(1 .. 3, []):
> for i to 2 do

   equns[i] := sum('uvec[j]*(diff(uvec[i], xvec[j]))', 'j' = 1 .. 2)

   end do;

the result the maple 11 gives is:
                     ...