In this paper, we present a log-based study on user search behavior comparisons on three different platforms: desktop, mobile and tablet. We use three-month search logs in 2012 from a commercial search engine for our study. Our objective is to better understand how and to what extent mobile and tablet searchers behave differently than desktop users. Our study spans a variety of aspects including query categorization, query length, search time distribution, search location distribution, user click patterns and so on. From our data set, we reveal that there are significant differences between user search patterns in these three platforms, and therefore use the same ranking system is not an optimal solution for all of them. Consequently, we propose a framework that leverages a set of domain-specific features, along with the training data from desktop search, to further improve the search relevance for mobile and tablet platforms. Experimental results demonstrate that by transferring knowledge from desktop search, search relevance on mobile and tablet can be greatly improved.