Extreme ultraviolet (EUV) waves, spectacular horizontally propagating disturbances in the low solar corona, always trigger horizontal secondary waves (SWs) when they encounter ambient coronal structure. We present a first example of upward SWs in a streamer-like structure after the passing of an EUV wave. The event occurred on 2017 June 1. The EUV wave happened during a typical solar eruption including a filament eruption, a CME, a C6.6 flare. The EUV wave was associated with quasi-periodic fast propagating (QFP) wave trains and a type II radio burst that represented the existence of a coronal shock. The EUV wave had a fast initial velocity of $sim$1000 km s$^{-1}$, comparable to high speeds of the shock and the QFP wave trains. Intriguingly, upward SWs rose slowly ($sim$80 km s$^{-1}$) in the streamer-like structure after the sweeping of the EUV wave. The upward SWs seemed to originate from limb brightenings that were caused by the EUV wave. All the results show the EUV wave is a fast-mode magnetohydrodynamic shock wave, likely triggered by the flare impulses. We suggest that part of the EUV wave was probably trapped in the closed magnetic fields of streamer-like structure, and upward SWs possibly resulted from the release of trapped waves in the form of slow-mode. It is believed that an interplay of the strong compression of the coronal shock and the configuration of the streamer-like structure is crucial for the formation of upward SWs.
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