JSFiddle - React, Tailwind, and code Playground
HTML
<link rel="stylesheet" href="http://code.jquery.com/mobile/1.0/jquery.mobile-1.0.min.css">
<script src="http://code.jquery.com/mobile/1.0/jquery.mobile-1.0.min.js"></script>
<div data-role="page" id="NY">
<div data-theme="a" data-role="header">
<h3>
</h3>
<div data-theme="d" data-role="header">
<h3>
<select name="select1" id="select1" data-mini="true" data-native-menu="false" class="navigateToPage">
<option value="NY">New York, NY</option>
<option value="SF">San Francisco, CA</option>
<option value="LV">Las Vegas, NV</option>
<option value="DAL">Dallas, TX</option>
</select>
</div>
</h3>
</div>
<div data-theme="a" data-role="footer">
</div>
</div>
<div data-role="page" id="SF">
<div data-theme="a" data-role="header">
<h3>
</h3>
<div data-theme="d" data-role="header">
<h3>
<select name="select2" id="select2" data-mini="true" data-native-menu="false" class="navigateToPage">
<option value="SF">San Francisco, CA</option>
<option value="NY">New York, NY</option>
<option value="LV">Las Vegas, NV</option>
<option value="DAL">Dallas, TX</option>
</select>
</div>
</h3>
</div>
<div data-theme="a" data-role="footer">
</div>
</div>
JavaScript
$(".navigateToPage").on('change', function() {
$(".navigateToPage").val($(this).val());
$(".navigateToPage").parent().find(".ui-btn-text").html($(this).find("option:selected").html());
});