Postgres 10 and partitioning by week
main manual doesn't help me a lot.


I hope you've read the manual, both entries:

ddl_partitioning (&amp; the Limitations 5.10.2.3. Limitations)

create table 

If yes, please mention specifically what you don't understand about it.


  partitioning natively... but what does it mean?


You don't have to create check constraints, trigger functions or triggers.

The SQL example above needs to be modified thusly:

e07=# CREATE TABLE public.audit_logs (
        log_type varchar(31) NOT NULL,
        id serial NOT NULL ,
        additional_data varchar(1024) NULL DEFAULT NULL::character varying,
        week int NOT NULL DEFAULT date_part('week', CURRENT_TIMESTAMP)
)
PARTITION BY list  (week) ;

--catch this error in the code:
--ERROR:  no partition of relation "audit_logs" found for row    



  and how to create auto tables public.audit_logs_N, where N would be week number?


Depending on the requirements, create the partitions in advance or use a pgagent (or crontab) to create them one at a time in the prior week.

create table audit_logs_not_1 partition of audit_logs for values in (1);
...
create table audit_logs_not_53 partition of audit_logs for values in (53);



  Do i need to create a trigger? or what?


A trigger is only needed for Implementation Using Inheritance