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In this paper we derive time-decay and Strichartz estimates for thegeneralized Benjamin-Bona-Mahony equation on the framework of modulation spaces$M^s_{p,q}.$ We use this results to analyze the existence of local and globalsolutions of the corresponding Cauchy problem with rough data in modulationspaces. The results improve known results in Sobolev spaces in some sense.

Time-decay and Strichartz estimates for the Benjamin-Bona-Mahony equation and existence of solutions on modulation spaces