<form class="art-search" method="get" name="searchform" action="<?php echo esc_url( site_url() ); ?>/">
    <input name="s" type="text" value="<?php echo esc_attr(get_search_query()); ?>" />
    <input class="art-search-button" type="submit" value="" />
</form>

(site)/new/?s=test *but does not return results.*

(site)/?s=test *returns all results.*