If you take a look at the HTML for an initialized data-type="search" widget you will see that the search form is pre-pended just before the list-view element:
<form class="ui-listview-filter ui-bar-c" role="search">
<div class="ui-input-search ui-shadow-inset ui-btn-corner-all ui-btn-shadow ui-icon-searchfield ui-body-c">
<input placeholder="Filter items..." data-type="search" class="ui-input-text ui-body-c">
<a href="#" class="ui-input-clear ui-btn ui-btn-up-c ui-btn-icon-notext ui-btn-corner-all ui-shadow ui-input-clear-hidden" title="clear text" data-theme="c">
<span class="ui-btn-inner ui-btn-corner-all">
<span class="ui-btn-text">clear text</span>
<span class="ui-icon ui-icon-delete ui-icon-shadow"></span>
</span>
</a>
</div>
</form>
<ul data-role="listview" data-filter="true" class="ui-listview">
<li data-theme="c" class="ui-btn ui-btn-icon-right ui-li-has-arrow ui-li ui-btn-up-c"><div class="ui-btn-inner ui-li"><div class="ui-btn-text"><a href="index.html" class="ui-link-inherit">Acura</a></div><span class="ui-icon ui-icon-arrow-r ui-icon-shadow"></span></div></li>
</ul>
So given this information you can see that to select the search input respectively to the list-view element you selector should looks something like this:
$("#search").prev().children().first().keyup(...)
Which selects the previous sibling element to the list-view (the <form class="ui-listview-finter"> element), then the first child of that element (), which should be the <input data-type="search" /> element. This is a pretty fast selector too, using an ID then single-level traversal functions.