# Can you someone please help to write last term of the first and third equation in the variational form
**URL:** https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298
**Category:** Feature Request
**Created:** [June 9, 2024, 8:31am UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298 "2024-06-09T08:31:37Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Monirul25](https://community.freefem.org/u/Monirul25)
#### Post date: [June 9, 2024, 8:31am UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298/1 "2024-06-09T08:31:37Z")
Here , is the variational form:
I have tried to write last term of the first equation and third equation in 2D but **i am getting product of two unknows present there which is not solvable by FreeFem++.**
**My trial** : (cv, nabla xi)=(c(v,vv), (xi\_{x}, xi\_{y}))
=((cv,cvv),(xi\_{x}, xi\_{y}))
=c_v_xi\_{x}+c_vv_ xi\_{y}), here product of two unkown is present.
Simillarly, i have tried for (c\*theta, nabla w)
Please help how write this term in linear form so that FF can solve easily using the command verf.
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### Author:  [@vlaude](https://community.freefem.org/u/vlaude)
#### Post date: [June 10, 2024, 7:14am UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298/2 "2024-06-10T07:14:23Z")
Dear Monirul,
The problem is non-linear (which is what you mean by ’ **i am getting product of two unknows** ’).
You must solve it iteratively. You may look at this example: [Newton Method for the Steady Navier-Stokes equations](https://doc.freefem.org/tutorials/navierStokesNewton.html#newton-method-for-the-steady-navier-stokes-equations)
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### Author:  [@Monirul25](https://community.freefem.org/u/Monirul25)
#### Post date: [June 10, 2024, 7:35am UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298/3 "2024-06-10T07:35:52Z")
I have seen this example. This is not helpful for my work as i have seen. There is no term in the equation you refer brother.
I need a equation where nable.(cv) term present where v is a vector in R^2. Moreover, if it is a non-linear term of one unknown then i can handel using fixed -point method. Here it is product of two unknowns.
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### Author:  [@vlaude](https://community.freefem.org/u/vlaude)
#### Post date: [June 10, 2024, 9:40am UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298/4 "2024-06-10T09:40:11Z")
The vector form of v is not an issue, just work with its components.
You need to linearize the equation first then apply Newton’s method. You can look for instance in these lecture notes: [https://www2.it.uu.se/edu/course/homepage/finmet2/vt13/lab2.pdf](https://www2.it.uu.se/edu/course/homepage/finmet2/vt13/lab2.pdf).
In the example I referred to, u is a vector and there are 3 unknowns (line 56, [du1, du2, dp]). In your case, you have 5 unknowns [c, mu, v1, v2, p].
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### Author:  [@DARBOUX](https://community.freefem.org/u/DARBOUX)
#### Post date: [April 13, 2026, 4:06pm UTC](https://community.freefem.org/t/can-you-someone-please-help-to-write-last-term-of-the-first-and-third-equation-in-the-variational-form/3298/5 "2026-04-13T16:06:28Z")
Good evening, could you please send me the link to the book? And please, where could I find a practical example of solving the Navier-Stokes equation on a moving domain ? Thank you.