<?php
// if data 'search' posted in POST method, make it safe in HTML then store it in $search. If 'search' data was not posted, fill it with an empty string ('')
$search = (isset($_POST['search'])) ? htmlentities($_POST['search']) : '';
?>
<form action="this_page.php" method="post">
<input type="text" name="search" placeholder="Search..." value="<?= $search ?>">
<input type="submit" value="Go">
</form>