One might expect DOMNode::lookupNamespaceURI( null ) to return the default namespace of the node (as the XML DOM spec indicates), but in fact it return nothing.
Added to this problem is the fact that DOMNode::getAttribute( 'xmlns' ) will not return the value of the xmlns attribute, so it is not possible to "walk" the tree back to find the default namespace.
As far as I can tell, there is no way in PHP 5 DOM to determine what the default namespace is in an XML document.