How to obtain CURDATE() / NOW() on a JPA named query?

That depends on your JPA provider. Hibernate, for example, supports current_date function:

from MyEntity where myDateProperty > current_date

From the spec:

4.6.16.3 Datetime Functions

functions_returning_datetime:=
CURRENT_DATE |
CURRENT_TIME |
CURRENT_TIMESTAMP

The datetime functions return the value of current date, time, and timestamp on the database server.