jquery-datepicker-set-default-date

Today date:

$( ".selector" ).datepicker( "setDate", new Date());
// Or on the init
$( ".selector" ).datepicker({ defaultDate: new Date() });

15 days from today:

$( ".selector" ).datepicker( "setDate", 15);
// Or on the init
$( ".selector" ).datepicker({ defaultDate: 15 });