# Convective term unsteady 2D NS equations

Hi everyone, I am implementing unsteady 2D Navier-Stokes equations but I am having troubles with the convective term.
Looking at the FreeFem documentation, I have found the built-in function convect that works pretty well for my kind of problem. The code that implements the convective term in this way is the following one:

``````varf navierstokes([ux, uy, p], [vx, vy, q])  = int2d(Th)(
rho/dt* [ux, uy]'* [vx, vy]
- p* div(v)
- q* div(u)
- 1e-10 *p*q
)
+ int2d(Th) (
[fx, fy]' * [vx, vy]
+ rho/dt* [convect([upx, upy], -dt, upx), convect([upx, upy], -dt, upy)]'* [vx, vy]
)
+ on(noslip, ux=0, uy=0)
+ on(inflow, ux=uin, uy=0)
;
``````

where up variables are the ones related to the previous time-step.
Thus, I have tried to directly implement the weak formulation of my problem, but it does not work. The related code is the following one:

``````varf navierstokes([ux, uy, p], [vx, vy, q])  = int2d(Th)(
rho/dt*  [ux, uy]'* [vx, vy]
- p* div(v)
- q* div(u)
- 1e-10 *p*q
)
+ int2d(Th) (
[fx, fy]' * [vx, vy]
- rho/dt* [upx,upy]'*[vx, vy]
)
+int2d(Th)(
)
+ on(noslip, ux=0, uy=0)
+ on(inflow, ux=uin, uy=0)
;
``````

Have someone ever had the same problem? Can you help me?