Disable live search only in 'menu'

If the site has live search enabled, what is the best practice to disable live search in the (mobile) drop down (navigation) menu:

Like this:

'Computer'

Home Folder1 Folder2 Contact | LiveSearch

Mobile

Regular Search [ Button ]
Home
Folder1
Folder2
Contact

To answer my own question:
Instead of disable the liveserch, just add two divs and enable live search on one one not on the other, then use CSS media queries to show hide them,...

Something like:
<form id="mobileonly searchform" data-action="@@search" action="@@search"> <input class="searchField" type="text" placeholder="Search Site" title="Search Site" size="15" name="SearchableText"> <button class="searchButton" type="submit"><i class="fa fa-search"> </i></button> </form>

and CSS
.mobileonly ( display: none; }

@media (max-width: 768px) {
.mobileonly ( display: block; }
.otherseachbox { display: none; }
}