Is my variational problem definition correct?

Hi, I am trying to solve following time dependent nonlinear problem

where u^j is the solution at jth time level and u^{j+1} is the solution at j+1 th time level. I’m stuck on define the problem in fenics. My definition for variational problem in Fenics is as follows

F = (inner((u - u_)/dt, v) + inner(u.dx(0)+u.dx(1),v) + inner(dot(u,nabla_grad(u)), v)+\
     inner((grad(u)-grad(u_))/dt, grad(v)))*dx

Can you give me feedback on whether it is true. İf it is not, what is its correct form?

Thank you.