So as the title says, I have always the same recurrent problem in chromium.
On default there's no search engine, so the url bar isn't a search bar, and it's useless, I have to go to google.com each time.

And when I want to add a new search engine, I put google, and I make it default and then everything works fine.

Until I log out.
And then there's no search engine, google has disapeared from the list.

I've had this problem since an upgrade some time ago.

My chromium version is 7.0.517.

Thanks for your help all and good night !