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Dynamic spectrum access by non-licensed users has emerged as a promising solution to address the bandwidth scarcity challenge. In a secondary spectrum market, primary users lease chunks of unused spectrum to secondary users. Auctions perform as one of the natural mechanisms for allocating the spectrum, generating an economic incentive for the licensed user to relinquish channels. Existing spectrum auction designs, while taking externality introduced by interference into account, fail to consider the potential mobility of secondary users, which leads to another dimension of externality: mobile communication motivates a secondary user to exclusively occupy a channel, i.e., forbidding channel reuse in its mobility region. In this work, we design two expressive auctions for mobility support, by introducing two-dimensional bids that reject a secondary user's willingness to pay for exclusive and non-exclusive channel usage, for the single-channel and multiple-channel scenarios, respectively. In the outcome of our 2D auctions, a channel is either monopolized or simultaneously reused without interference, whereas a secondary user can be mobile or is regulated to be static. We prove the existence of desirable equilibria in both auctions, where 1/10 and c/7(1+c) of optimal social welfare are guaranteed to be recoverable, respectively (c is the number of channels).