No Search results for some users not default zones

Hi,

I configured 02 zones for the same web applications:

1) Default: with Windows integrated authentication

2) Intranet: With ADFS authentication and is the only zone published.

The users connect only to the intranet zone and i configured the search to crawl the default zone.

The problem is that i don't get any search result when i am connected in the intranet zone (but i get results when i am connected to the default zone).

Can anyone help to figure out a solution ?

thanks

Edit: after some tests, it seems that this problem concerne only some users, but i don't understand why(it doesn't work vor the site collection admin)

PS. I prefer to avoid using a mixed authentication as described HERE