<form method='get' action='https://google.com/search' rel='nofollow' target='_blank'>
  <input type='hidden' name='sitesearch' value='mywebsite.com' />
  <input type='search' name='q' placeholder='search via Google' />
  <button title='search (opens in new tab)' type='submit' value='submit'>Search</button>
</form>